SOLUTION: One leg of a right triangle is 4 inches longer than the other. The hypotenuse of the triangle is 8 inches longer than the shorter leg. What are the lengths of the 3 sides of the tr
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Question 1124029: One leg of a right triangle is 4 inches longer than the other. The hypotenuse of the triangle is 8 inches longer than the shorter leg. What are the lengths of the 3 sides of the triangle? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a^2 + b^2 = c^2
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One leg of a right triangle is 4 inches longer than the other.
a = b + 4
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The hypotenuse of the triangle is 8 inches longer than the shorter leg.
c = b + 8
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What are the lengths of the 3 sides of the triangle?
replace a & c in the formula
(b+4)^2 + b^2 = (b+8)^2
FOIL
b^2 + 8b + 16 + b^2 = b^2 + 16b + 64
Combine like terms on the left
b^2 + b^2 - b^2 + 8b - 16b + 16 - 64 = 0
b^2 - 8b - 48 = 0
Factors to
(b-12)(b+4) = 0
the positive solution is all we want here
b = 12
then, obviously
a = 16
c = 20
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Check on your calc:
