document.write( "Question 206204: The area of a right triangle is 120 sq. in. The longer leg is 4 more than twice the shorter leg. Find the length of each leg. Show all work to receive credit.
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Algebra.Com's Answer #155761 by Marth(57) $\"\"$ $\"About$

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For a triangle, $\"A=%281%2F2%29bh\"$
\n" ); document.write( "Because it is a right triangle, the two legs are the base and height.
\n" ); document.write( "let x = the shorter leg
\n" ); document.write( "2x+4 = the longer leg
\n" ); document.write( " $\"120+=+%281%2F2%29%28x%29%282x%2B4%29\"$
\n" ); document.write( " $\"240=2x%5E2%2B4x\"$
\n" ); document.write( " $\"2x%5E2%2B4x-240=0\"$
\n" ); document.write( "Divide by 2.
\n" ); document.write( " $\"x%5E2%2B2x-120=0\"$
\n" ); document.write( "Factor.
\n" ); document.write( " $\"%28x%2B12%29%28x-10%29=0\"$
\n" ); document.write( " $\"%28x%2B12%29=0\"$ or $\"%28x-10%29=0\"$
\n" ); document.write( " $\"x=-12\"$ or $\"x=10\"$
\n" ); document.write( "The side length canot be negative, so ignore $\"x=-12\"$
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\n" ); document.write( "The shorter leg has length 10in, and the longer leg has length $\"2%2810%29%2B4\"$ = 24in \n" ); document.write( "

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