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

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In a discussion about finding the side lengths of a Pythagorean triangle ABC with an area of 8214 and an inscribed square DEFG with side lengths of 60, participants focused on the geometric relationships involved. The square's side DE lies along the hypotenuse of the triangle, prompting calculations to determine the triangle's dimensions. The conversation included playful banter, but the main objective remained centered on solving for the triangle's side lengths based on the given area and square dimensions. The problem emphasizes the application of the Pythagorean theorem in conjunction with area considerations. Ultimately, the goal is to derive the exact lengths of the triangle's sides.
Wilmer
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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
 
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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
 
Wilmer said:
Formula:
d = abc / (a^2 + b^2 + ab)

Where did you get it?
 
Monoxdifly said:
Where did you get it?
Made it up...
 
Duh...
 
Monoxdifly said:
Duh...
Deaf Upon Hearing ?
 
Wilmer said:
Deaf Upon Hearing ?

Dumb Upon Hearing
 

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