SOLUTION: One leg of a right triangle is 4cm shorter thatn the other leg. The length of the hypotenuse is 20 cm. Find the length of the shorter leg. A. 16cm B. 17cm C. 13cm D. 12cm

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Question 22895: One leg of a right triangle is 4cm shorter thatn the other leg. The length of the hypotenuse is 20 cm. Find the length of the shorter leg.
A. 16cm
B. 17cm
C. 13cm
D. 12cm
Answer by wuwei96815(245) About Me  (Show Source):
You can put this solution on YOUR website!
Right triangle formula is a^2 + b^2 = c^2.

(x)^2 + (x-4)^2 = (20)^2
x^2 + x^2 -8x +16 = 400
2x^2 -8x + 16 = 400
2(x^2-4x+8) = 400
x^2-4x+8 = 200
x^2-4x-192 = 0
(x-16)(x+12) =0

The solutions for x are 16 and -12. We can ignore the -12 answer. So, x=16 and the shorter leg is x-4 or 12.

I hope that you were able to follow the solution.