# 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, 3 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 $$\left(\frac{8}{3}\right)^2=\frac{64}{9}$$

- 3 years, 3 months ago

yes

how did you do it

- 3 years, 3 months ago

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

- 3 years, 3 months ago

But how to maximize

- 3 years, 3 months ago

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 .

- 3 years, 3 months ago

so

- 3 years, 3 months ago

Please could you give the full solution

- 3 years, 3 months ago

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 $$\dfrac{8}{3}$$

- 3 years, 3 months ago

Thanks! a lot

- 3 years, 3 months ago

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

- 3 weeks ago

All are same.

- 2 weeks, 5 days ago

@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

- 1 week ago

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

- 6 days, 6 hours ago

aap allen ke hostel me rehte ho

- 3 days, 19 hours ago

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

- 4 days, 7 hours ago

DDPS

- 4 days, 7 hours ago

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

- 3 days, 19 hours ago

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

- 3 days, 19 hours ago

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

- 4 days, 7 hours ago

I don't know fees, Board is CBSE.

- 4 days, 7 hours ago

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.

- 3 days, 19 hours ago

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

- 3 days, 14 hours ago

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.

- 19 hours ago

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

- 14 hours ago

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 .

- 3 days, 19 hours ago

You can call them up and ask. Fee Structure

- 3 days, 14 hours ago

- 1 week ago

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

- 1 month, 2 weeks ago

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.

- 1 month, 2 weeks ago

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

- 1 month, 2 weeks ago

yeah

- 1 month, 2 weeks ago

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

- 3 weeks, 1 day ago

If in class 11 then should do JEE else both.

- 3 weeks, 1 day ago

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

- 3 weeks, 1 day ago

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

- 3 weeks, 1 day ago

are u still in kota

- 1 month, 2 weeks ago

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

- 1 month, 3 weeks ago

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

- 1 month, 3 weeks ago

- 1 month, 3 weeks ago

what moderator means and how to be a moderator

- 1 month, 3 weeks ago

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.

- 1 month, 3 weeks ago

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

- 1 month, 3 weeks ago

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

- 1 month, 3 weeks ago

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

- 1 month, 3 weeks ago

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

- 1 month, 3 weeks ago

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

- 1 month, 3 weeks ago

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 $$\frac{64}{9}$$

- 3 years, 3 months ago

See this problem.

Staff - 3 years, 3 months ago

Could you elaborate his solution @Calvin Lin

- 3 years, 3 months ago

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

Staff - 3 years, 3 months ago

Comment deleted Jan 08, 2015

Comment deleted Jan 08, 2015

- 3 years, 3 months ago

could you tell me your approach

- 3 years, 3 months ago