document.write( "Question 318709: a right triangle has an area of 60 m^2 and the hypotenuse is 2 m longer than the longer side of 2 remaining legs. Can you please find the dimensions of the triangle? \n" ); document.write( "

Algebra.Com's Answer #228202 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. $\"A=%281%2F2%29L1%2AL2=60\"$
\n" ); document.write( "2. $\"H=L2%2B2\"$
\n" ); document.write( "From the Pythagorean theorem,
\n" ); document.write( "3. $\"L1%5E2%2BL2%5E2=H%5E2\"$
\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"L1%2AL2=120\"$
\n" ); document.write( " $\"L1=120%2FL2\"$
\n" ); document.write( "Substitute into eq. 3,
\n" ); document.write( " $\"%28120%2FL2%29%5E2%2BL2%5E2=%28L2%2B2%29%5E2\"$
\n" ); document.write( " $\"%28120%2FL2%29%5E2%2BL2%5E2=L2%5E2%2B4L2%2B4\"$
\n" ); document.write( " $\"%2814400%2FL2%5E2%29=4L2%2B4\"$
\n" ); document.write( " $\"14400=4L2%5E3%2B4L%5E2\"$
\n" ); document.write( " $\"L2%5E3%2BL2%5E2-3600=0\"$
\n" ); document.write( "You can factor this equation,
\n" ); document.write( " $\"%28L2-15%29%28L2%5E2%2B16L2%2B240%29=0\"$
\n" ); document.write( "One real solution:
\n" ); document.write( " $\"L2-15=0\"$
\n" ); document.write( " $\"highlight%28+L2=15%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"L1=120%2F15\"$
\n" ); document.write( " $\"highlight%28+L1=8%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"H=L2%2B2\"$
\n" ); document.write( " $\"highlight%28+H=17+%29\"$
\n" ); document.write( " \n" ); document.write( "

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