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Square in triangle...

Wilmer

In Memoriam
Mar 19, 2012
376
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
 

Wilmer

In Memoriam
Mar 19, 2012
376
In case I lose it!
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

Well-known member
Aug 6, 2015
271

Wilmer

In Memoriam
Mar 19, 2012
376

Monoxdifly

Well-known member
Aug 6, 2015
271
Duh...
 

Wilmer

In Memoriam
Mar 19, 2012
376

Monoxdifly

Well-known member
Aug 6, 2015
271