SOLUTION: The hypotenuse of a right triangle is 16 inches longer than the shortest side and 8 inches longer than the remainig side. Find the dimensions of the triangle

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Question 287402: The hypotenuse of a right triangle is 16 inches longer than the shortest side and 8 inches longer than the remainig side. Find the dimensions of the triangle
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The hypotenuse of a right triangle is 16 inches longer than the shortest side and
8 inches longer than the remaining side.
Find the dimensions of the triangle
:
Let x = the hypotenuse
then
(x-16) = one side
and
(x-8) = remaining side
:
Using pythag: a^2 + b^2 = x^2
:
(x-16)^2 + (x-8)^2 = x^2
FOIL
x^2 - 32x + 256 + x^2 - 16x + 64 = x^2
Combine like terms
x^2 + x^2 - x^2 - 32x - 16x + 256 + 64 = 0
:
x^2 - 48x + 320 = 0
Factor
(x-40)(x-8) = 0
:
x = 40, the hypotenuse (the only solution that will fit this problem)
then
40 - 16 = 24; one side
and
40 - 8 = 32; remaining side
:
:
Check:
24^2 + 32^2 = 40^2
576 + 1024 = 1600