document.write( "Question 853239: The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle \n" ); document.write( "

Algebra.Com's Answer #513957 by hovuquocan1997(83) $\"\"$ $\"About$

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Let the long leg of this right triangle be \"x\"
\n" ); document.write( "Then you will have the short leg is \"x-5\" and the hypotenuse is \"x+5\"
\n" ); document.write( "Use Pythagorean Theorem, you will have:
\n" ); document.write( " $\"%28x-5%29%5E2+%2B+x%5E2+=+%28x%2B5%29%5E2\"$
\n" ); document.write( " $\"x%5E2+-10x+%2B+25+%2B+x%5E2+=+x%5E2+%2B+10x+%2B+25\"$
\n" ); document.write( " $\"2x%5E2+-+10x+%2B+25+=+x%5E2+%2B+10x+%2B+25\"$
\n" ); document.write( " $\"x%5E2+-+20x+=+0\"$
\n" ); document.write( " $\"x%28x-20%29+=+0\"$
\n" ); document.write( "x = 0 or x = 20
\n" ); document.write( "But since a side of a triangle can't be 0, x=20
\n" ); document.write( "So you have the long leg of the triangle is 20
\n" ); document.write( "The short leg will be 20-5 = 15
\n" ); document.write( "The hypotenuse will be 20+5 = 25
\n" ); document.write( "TA-DAH
\n" ); document.write( ":D \n" ); document.write( "

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