document.write( "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!! \n" ); document.write( "

Algebra.Com's Answer #716773 by hovuquocan1997(83) $\"\"$ $\"About$

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Based on the Pythagorean Theorem, we can label the two legs x and y and have:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2+%2B+y%5E2+=+8%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "However, because the two legs are equal, x = y and we can substitute x in for y:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2+%2B+x%5E2+=+8%5E2\"$
\n" ); document.write( " $\"2x%5E2+=+64\"$
\n" ); document.write( " $\"x%5E2+=+32\"$
\n" ); document.write( " $\"x+=+sqrt%2832%29\"$
\n" ); document.write( " $\"x+=+4sqrt%282%29\"$ \r
\n" ); document.write( "\n" ); document.write( "So both legs are $\"4sqrt%282%29\"$ because they are equal :). \n" ); document.write( "

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