Square in the triangle problem

[theme21]

So I've found this interesting problem but couldn't solve it. Some help?


A square has been inscribed into a rectangular triangle like on the picture below. If the hypotenuse of the triangle c=35, and the side of the square a=12, find the remaining two sides of the triangle.

If anyone could help, I'd be grateful

 

[Deleted member 4993]

So I've found this interesting problem but couldn't solve it. Some help?


A square has been inscribed into a rectangular triangle like on the picture below. If the hypotenuse of the triangle c=35, and the side of the square a=12, find the remaining two sides of the triangle.

If anyone could help, I'd be grateful

Hint: Use similar triangle theorems and Pythagorean theorems.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[stapel]

A square has been inscribed into a rectangular triangle like on the picture below.

A
| \
|D  \ E
*----* 
|    | \
|    |   \
*----*----*
B    F     C

If the hypotenuse AC of the triangle has length 35, and the side DB of the square has length 12, find the lengths of the remaining two sides of the triangle.

I've labelled things, so we can speak clearly.

You have a square BDEF which splits two triangles, ADE and EFC, from the original triangle ABC. By nature of squares, you know the angles at the corners of BDEF, and you know that the sides DE and EF are parallel, respectively, to sides AB and BC. So what can you say about the angles and side-length ratios of the original triangle and the two new triangles?

You are given that AC has length 35. You are given that DB = BF = FE = DE = 12. Can you set up some proportions with this information, together with what you have from the previous paragraph?

If you get stuck, please reply showing all of your work so far. Thank you!