SOLUTION: One leg of a right triangle is 5 cm shorter than the other leg. The length of the hypotenuse is 25 cm. Find the length of the shorter leg.

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Question 242848: One leg of a right triangle is 5 cm shorter than the other leg. The length of the hypotenuse is 25 cm. Find the length of the shorter leg.
Answer by unlockmath(1688) (Show Source):
You can put this solution on YOUR website!
Hello,
Let's have x represent one leg and the shorter leg be x-5.
The formula a^2 + b^2 = C^2 (C is the hypotenuse) With what we know we can put in the data.
x^2 + (x-5)^2 = 25^2 Expanding this out will look like:
x^2 + x^2 -10x +25 = 625 Combine like terms and subtract 625 from both sides gives us:
2x^2 -10x - 600 = 0 or can be rewritten as:
2(x^2 -5x -300)= 0 This can be factored as:
2(x-20)(x+15)=0
x=20
x=-15
20 makes sense for the answer. So the shorter leg is 15cm
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