SOLUTION: A brace for a shelf has the shape of a right triangle. Its hypotenuse is 8 inches long and the two legs are equal in length. How long are the legs of the​ triangle? Simplif

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Question 1102136: A brace for a shelf has the shape of a right triangle. Its hypotenuse is 8 inches long and the two legs are equal in length. How long are the legs of the​ triangle? Simplify your answer. Type a radical expression in lowest terms. THANK YOU!!
Answer by hovuquocan1997(83) About Me  (Show Source):
You can put this solution on YOUR website!
Based on the Pythagorean Theorem, we can label the two legs x and y and have:
x%5E2+%2B+y%5E2+=+8%5E2
However, because the two legs are equal, x = y and we can substitute x in for y:
x%5E2+%2B+x%5E2+=+8%5E2
2x%5E2+=+64
x%5E2+=+32
x+=+sqrt%2832%29
x+=+4sqrt%282%29
So both legs are 4sqrt%282%29 because they are equal :).