Pythagorean Fun!

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,689
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.
Code:
B

         E


                     D

F



C         G                               A
 

Otis

Senior Member
Joined
Apr 22, 2015
Messages
1,387
I started with triangle CGF isosceles (which gives 8100 for area of triangle ABC) and then rotated the square, using angle CGF as a parameter. With symmetry identities, the adjustments to AC and BC were easy enough, but then I got lazy and used technology to solve my equation.

My answer: 111, 148, 185
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,689
Yepper!
a = BC, b=AC, c = AB, d = square side
Formula:
d = abc / (a^2 + b^2 + ab)
111*148*185 / (111^2 + 148^2 + 111*148) = 60

However, wrote looper program to solve...
 
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