SOLUTION: the hypotenuse of a right triangle is 8feet less then three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides

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Question 455467: the hypotenuse of a right triangle is 8feet less then three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of the ttriangle.
Answer by nerdybill(7384) About Me  (Show Source):
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the hypotenuse of a right triangle is 8feet less then three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of the ttriangle.
.
Let x = shorter leg
then
3x-8 = hypotenuse
2x+8 = longer leg
.
applying Pythagorean theorem:
x^2 + (2x+8)^2 = (3x-8)^2
x^2 + (2x+8)(2x+8) = (3x-8)(3x-8)
x^2 + (4x^2+16x+16x+64) = (9x^2-24x-24x+64)
x^2 + 4x^2+32x+64 = 9x^2-48x+64
5x^2+32x+64 = 9x^2-48x+64
32x+64 = 4x^2-48x+64
64 = 4x^2-80x+64
0 = 4x^2-80x
0 = x^2-20x
0 = x(x-20)
x = {0, 20}
throw out the zero leaving
x = 20 feet (shorter leg)
.
hypotenuse:
3x-8 = 3(20)-8 = 60-8 = 52 feet
.
longer leg:
2x+8 = 2(20)+8 = 40+8 = 48 feet