pls help Math question

please help me with the math problem \[The\quad area\quad of\quad the\quad largest\quad square\quad which\quad can\quad be\\ inscribed\quad in\quad a\quad right\quad angled\quad triangle\quad with\quad legs\\ 4\quad units\quad and\quad 8\quad units\quad is\]

Note by Rajdeep Dhingra
3 years, 11 months ago

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I used some simple analitical geometry and get the side of the square is \(\frac{8}{3}\) and thus the area is \(\left(\frac{8}{3}\right)^2=\frac{64}{9} \)

Poetri Sonya - 3 years, 11 months ago

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yes

how did you do it

Rajdeep Dhingra - 3 years, 11 months ago

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Just put the triangle in the Cartesian diagram with the coordinates are (0,0),(4,0) and(0,8)

Poetri Sonya - 3 years, 11 months ago

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@Poetri Sonya But how to maximize

Rajdeep Dhingra - 3 years, 11 months ago

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@Rajdeep Dhingra The largest square in the triangle is when the square's coordinates are \((0,0),(0,x),(x,0)\)and\((x,x)\) with \((x,x)\) lies in the hypotenuse .

Poetri Sonya - 3 years, 11 months ago

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@Poetri Sonya so

Rajdeep Dhingra - 3 years, 11 months ago

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@Poetri Sonya Please could you give the full solution

Rajdeep Dhingra - 3 years, 11 months ago

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@Rajdeep Dhingra Since \((x,x)\) lies in the hypotenuse, it lies in the line \(y=-2x+8\). Then \[x=-2x+8\] \[3x=8\] \[x=\frac{8}{3}\] So the side is \(\dfrac{8}{3}\)

Poetri Sonya - 3 years, 11 months ago

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@Poetri Sonya Thanks! a lot

Rajdeep Dhingra - 3 years, 11 months ago

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pls help me with the provided question

Om Tiwari - 4 months ago

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Two particles of mass m and M undergo uniform circular motion about each other at a separation R under the influence of an attractive constant force F. The angular velocity is ω radians per second. Show that R = (F/ω2)(1/m + 1/M)..

Om Tiwari - 4 months ago

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@Rajdeep Dhingra I want to buy EM Purcell and Morin Elcetricity and Magnetism in Paperback edition or to download it ;hardcover edition is there or pls bhaiya just share it if you have through internet i.e provide me the link

Om Tiwari - 4 months ago

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what i should do to get the answer of that vector problem in my book .i don't know how to post a multi correct answer type questons

Brilliant Member - 7 months, 4 weeks ago

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@Rajdeep Dhingra i think you have done a mistake their magnitudes have to be different pls reply if you got a new intuition or thought process behind the problem .the same ques was published by resonance coaching in their test paper for jee advanced

Brilliant Member - 7 months, 4 weeks ago

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PLS REPLY

Brilliant Member - 7 months, 4 weeks ago

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@Rajdeep Dhingra can you write what you thought for solving the problem or u directly thought their magnitudes can be all of them we have to select them so that all of them adjusts for answer to be all respective options

Brilliant Member - 7 months, 4 weeks ago

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@Rajdeep Dhingra can you write what you thought for solving the problem or u directly thought their magnitudes can be all of them we have to select them so that all of them adjusts for answer to be all respective options

Brilliant Member - 7 months, 4 weeks ago

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Comment deleted 7 months ago

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You can make A,B,C = 0 if you take Equal magnitudes , so any extra A will increase magnitude to be whatever you want.

Rajdeep Dhingra - 7 months, 4 weeks ago

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pls reply

Brilliant Member - 7 months, 4 weeks ago

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hope you read what i wrote just a minute ago

Brilliant Member - 7 months, 4 weeks ago

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sorry i think you did a slight wrong i also thought in a similar way but again read the ques they have different magnitudes but in your examples they have same magnitudes atleast two of them have and to this problem my old book of balaji publications offers no solution and also no option as answer

Brilliant Member - 7 months, 4 weeks ago

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thank u actually i got in this problem in some old book of balaji publications but since it was subjective answer was not given

Brilliant Member - 7 months, 4 weeks ago

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pls explain me well you can also give me link of imgur if written on copy

Brilliant Member - 7 months, 4 weeks ago

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@Rajdeep Dhingra pls help me in this question if sum of three unit ,coplanar vectors is equal to 0 i.e. Â+Ŷ+Ê=0.and if vector p,q and r are parallel to vectors A,Yand E respectively.p.q and r have integral but different magnitudes then |vec p + vec q + vec r| can be = to options:

1.)root 3

2.)root 2

3.)1

4.)0

ques type (ONE OR MORE IS CORRECT)

Brilliant Member - 7 months, 4 weeks ago

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All are correct.

Rajdeep Dhingra - 7 months, 4 weeks ago

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can u explain how

Brilliant Member - 7 months, 4 weeks ago

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@Brilliant Member Examples , p = 1+sqrt(3) A, q = 1 B, r = 1 C p= 1+sqrt(2) A, q= 1B , r = 1C p= 2 A , q=1B , r= 1C p= 1 A , q= 1 B , r = 1C

Rajdeep Dhingra - 7 months, 4 weeks ago

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@Rajdeep Dhingra can u write which corresponds to which option like ur first example corresponds to which one it would be easy to check

Brilliant Member - 7 months, 4 weeks ago

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@Brilliant Member It is the order only.

Rajdeep Dhingra - 7 months, 4 weeks ago

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@Rajdeep Dhingra PLS REPLY IF U HAVE SOLVED IT IN EXAMPLES THEY HAVE SAME MAGNITUDES AND ALSO IN YOUR METHOD THEY ARE HAVING SAME MAGNITUDES A,B,C=0. ATLEAST QUES. IF QUES. IS LACKING INFO. ACCORDING TO ME IT IS LACKING SO.

Brilliant Member - 7 months, 3 weeks ago

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@Rajdeep Dhingra they have same magnitudes atleast two of them have if u have solved then pls explain or reply .pls reply

Brilliant Member - 7 months, 4 weeks ago

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@Rajdeep Dhingra thanks that i made

Brilliant Member - 7 months, 4 weeks ago

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@Brilliant Member pls explain me asap

Brilliant Member - 7 months, 4 weeks ago

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@Brilliant Member why are u silent pls if u know the thought process explain me this

Brilliant Member - 7 months, 4 weeks ago

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Bhaiya which book would be better for physics halliday resnick and krane,halliday,resnick and walker or university physics by sears and zemansky or physics for scientists and engineers by serway and jewett regarding ipho and for proper understanding

Brilliant Member - 8 months, 3 weeks ago

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All are same.

Rajdeep Dhingra - 8 months, 2 weeks ago

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@Rajdeep Dhingra Bhaiya i want to know if it is possible to pursue studies from shiv jyoti convent in kota from another city and waht is the fees of ddps kota class 11 pcm 1 month. pls can u give me the(URL) link or list some dummy schools with minimum fees range.pls reply asap .pls help me

Brilliant Member - 8 months ago

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@Brilliant Member I don't know , but DDPS , Shiv Jyoti , Maha Bharti Kota , these all are dummy.

Rajdeep Dhingra - 8 months ago

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@Rajdeep Dhingra aap allen ke hostel me rehte ho

Brilliant Member - 8 months ago

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@Rajdeep Dhingra u r pursuing ur studies from which school,if it is associated with allen

Brilliant Member - 8 months ago

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@Brilliant Member DDPS

Rajdeep Dhingra - 8 months ago

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@Rajdeep Dhingra i was amazed to see this while searching https://timesofindia.indiatimes.com/city/jaipur/HC-notice-to-govt-school-boards-coaching-institutes/articleshow/40073991.cms

Brilliant Member - 8 months ago

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@Rajdeep Dhingra actually the problem is that i am looking for dummy school but in ,my city Lko. schools are dummy in each and every aspect like not even a single school of cbse is dummy and on going through internet i got to know that in kota almost all schools are dummy

Brilliant Member - 8 months ago

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@Brilliant Member what is fees of ur school and which board .pls answer

Brilliant Member - 8 months ago

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@Brilliant Member I don't know fees, Board is CBSE.

Rajdeep Dhingra - 8 months ago

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@Rajdeep Dhingra DDPS is a dummy therefore i think not even once in a month one goes there during pre-board or exams one has to go there or i if i am wrong then pls do write correct info. is it required to attend the school weeklies i.e. 1 day in a week.

Brilliant Member - 8 months ago

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@Brilliant Member I don't know these things , but I think you have to go once a month or something.

Rajdeep Dhingra - 8 months ago

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@Rajdeep Dhingra How many times you attend the school i.e.(DDPS) once in a week or in 2 weeks period.I wanted to know it on an average which means how many days per month.

Brilliant Member - 8 months ago

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@Brilliant Member I don't know so much detail. Just call them and ask.

Rajdeep Dhingra - 7 months, 4 weeks ago

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@Rajdeep Dhingra can you ask from someone fees of DDPS for me class 11 because it is no longer possible for me to get all information like fees from here Lucknow.I am only dependent on you and these two websites brilliant and quora for my answers .

Brilliant Member - 8 months ago

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@Brilliant Member You can call them up and ask. Fee Structure

Rajdeep Dhingra - 8 months ago

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@Brilliant Member pls answer

Brilliant Member - 8 months ago

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Rajdeep bhaiya in which school u r currently studying.is it worth to join a dummy school for 11th and 12th

Brilliant Member - 9 months, 2 weeks ago

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It is really difficult to answer such questions. Such things are based on school to school , child to child so you really have to decide it yourself.

Rajdeep Dhingra - 9 months, 2 weeks ago

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u r absolutely correct is shiv jyoti in rajeev nagar,kota a dummy one

Brilliant Member - 9 months, 2 weeks ago

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@Brilliant Member yeah

Rajdeep Dhingra - 9 months, 2 weeks ago

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@Rajdeep Dhingra IS IT ADVISABLE TO PREPARE FOR IMO (HBCSE )ONE WITH JEE PREPARATION .WHAT U WOULD RECOMMEND OR SUGGEST TO PURSUE BOTH OF THEM OR EITHER OF THEM i.e. latter or former one

Brilliant Member - 8 months, 3 weeks ago

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@Brilliant Member If in class 11 then should do JEE else both.

Rajdeep Dhingra - 8 months, 3 weeks ago

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@Rajdeep Dhingra i actually want to pursue physics as my interest as future career especially to do some sort of research and truly speaking i also want to master mathematics to migrate to higher physics as well as without latter it would be almost impossible to do so .and i know that whatever is in imo is for mathematics and in modern physics or even in classical one demads a nice hold over calculus which is not at all in imo

Brilliant Member - 8 months, 3 weeks ago

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@Rajdeep Dhingra not in 11 th but as of now getting my hands cleaned off the boards i am promoted to class 11 and were u able to make out to inmo if so then suggest me books

Brilliant Member - 8 months, 3 weeks ago

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@Rajdeep Dhingra are u still in kota

Brilliant Member - 9 months, 2 weeks ago

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pls rajdeep bhaiya tell me about moderator and how to be so

Brilliant Member - 9 months, 3 weeks ago

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Rajdeep bhaiya how did u subscribe to brilliant premium and at what cost

Brilliant Member - 9 months, 3 weeks ago

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I am a moderator so I get it for free.

Rajdeep Dhingra - 9 months, 3 weeks ago

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what moderator means and how to be a moderator

Brilliant Member - 9 months, 3 weeks ago

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@Brilliant Member Agnishom has nicely explained what is a moderator Here. To be a moderator , a staff member will pick you , you will be selected as seen by your activity on brilliant , helping out others and things like that.

Rajdeep Dhingra - 9 months, 3 weeks ago

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@Rajdeep Dhingra bhaiya in which school u did ur class 10th is it a dummy one

Brilliant Member - 9 months, 3 weeks ago

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@Brilliant Member I did half 10th in DPS Mathura Road and half in DDPS.

Rajdeep Dhingra - 9 months, 3 weeks ago

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@Rajdeep Dhingra sorry for 'why' i am not interested in that but what u think about dummy schools because i think one can't get enough time to prepare for olympiads and all from the pulls and pressures of the schools

Brilliant Member - 9 months, 3 weeks ago

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@Rajdeep Dhingra why so is ddps a dummy and cbse board and now in which school

Brilliant Member - 9 months, 3 weeks ago

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@Brilliant Member can someone tell me about "moderator" and how to be so pls its a request

Brilliant Member - 9 months, 3 weeks ago

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This the procedure to do this kind of a sum:

Let the side of the required square be \(a\).

Length of the remaining parts of the two legs are respectively \(8-a\) and \(4-a\).

So the total area which is \(\frac{1}{2}.a.(8-a)+a^{2}+\frac{1}{2}.a.(4-a)\) will be equal to \(16\) (the area of the whole triangle)

Solving the equation you get \(x=\frac{8}{3}\)

and hence the area is \(\frac{64}{9}\)

Anik Mandal - 3 years, 11 months ago

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See this problem.

Calvin Lin Staff - 3 years, 11 months ago

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Could you elaborate his solution @Calvin Lin

Rajdeep Dhingra - 3 years, 11 months ago

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You should comment on his solution and ask him to clarify.

Calvin Lin Staff - 3 years, 11 months ago

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Comment deleted Jan 08, 2015

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Comment deleted Jan 08, 2015

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Sorry i misread the question

Soutrik Bandyopadhyay - 3 years, 11 months ago

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@Soutrik Bandyopadhyay could you tell me your approach

Rajdeep Dhingra - 3 years, 11 months ago

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