I cannot find the specific problem but it summarized as follows:

Isosceles triangle $ABC$ with $AB=AC$ and $BC=60$.

A point $D$ on base $BC$ is located such that a perpendicular to side $AB$, denoted as $DE$, has length 16 and a perpendicular to side $AC$, denoted as $DF$, has length 32. Points $E$ and $F$ are on $AB$ and $AC$ respectively. What is the length of the two equal sides of triangle $ABC$?

The correct answer shown was 50. I got a different answer using similar triangles etc. I checked and rechecked and continued to get my original answer. I then constructed the posted answer graphically and while the one perpendicular was equal to 16, it resulted in the other perpendicular being ~38.75.

In my answer, each of the two equal sides were ~43.148. Moreover, when I graphed the problem, the two perpendiculars measured 16 and 32 respectively.

At this point, I am wondering if my rendering of the image is wrong as no drawing was included in the problem.

No vote yet

1 vote

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in`\(`

...`\)`

or`\[`

...`\]`

to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestLet point $G$ be foot of perpendicular from A on $BC$. $\triangle EBD$ is similar to $\triangle DFC$ and to $\triangle BGA$. $BD=20, BE=12, AG=40, AB=50$

It looks like the answer is in fact 50.

Log in to reply

Can you include a drawing? If point D is on the base then BE cant be 12 sonce it the hypotenuse of triangle EDB

Log in to reply

I uploaded the image here

Log in to reply

Log in to reply