Solve for equal sides of isosceles triangle given base and two perpendiculars from base to the two sides

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.

#Geometry

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:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Let 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.

Maria Kozlowska - 5 years, 3 months ago

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

Greg Grapsas - 5 years, 3 months ago

I uploaded the image here

Maria Kozlowska - 5 years, 3 months ago

@Maria Kozlowska – Thank you...when i saw it i realized my stupid mistake...i had df correct but i foolishly had DE perpendicular to the base instead of BA and just couldnt see it until you sent me the drawing

Greg Grapsas - 5 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$