MHB Find Side Lengths of Pythagorean Triangle ABC with Square DEFG Inscribed

[Wilmer]

Pythagorean triangle ABC with area 8214
has square DEFG with sides = 60 inscribed in it.
Side DE of the square lies on the hypotenuse.
Find the triangle's side lengths.

B

         E                     D

F
C         G                               A

 

[Wilmer]

In case I lose it!

Spoiler

a = BC, b = AC, c = AB, d = square side
Formula:
d = abc / (a^2 + b^2 + ab)

Solution: a = 111, b = 148, c = 185

111 * 148 / 2 = 8214

 

[Monoxdifly]

Spoiler

Formula:
d = abc / (a^2 + b^2 + ab)

Where did you get it?

 

[Wilmer]

Where did you get it?

Made it up...

 

[Monoxdifly]

Duh...

 

[Wilmer]

Duh...

Deaf Upon Hearing ?

 

[Monoxdifly]

Deaf Upon Hearing ?

Dumb Upon Hearing