document.write( "Question 455886: A room has a shape of a right triangle. One of the legs of the triangle is one meter longer than the other. The perimeter of the room is 12 meters. What are the lengths of the three sides? \n" ); document.write( "

Algebra.Com's Answer #312958 by Gogonati(855) $\"\"$ $\"About$

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Let's the smaller leg = x m, then the other leg is (x+1) m and the hypotenuse is\r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%28x%5E2%2B%28x%2B1%29%5E2%29\"$ m.Since the perimeter is 12 m we write the equation:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2Bx%2B1%2Bsqrt%28x%5E2%2B%28x%2B1%29%5E2%29=12\"$ . We now solve this equation.\r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%282x%5E2%2B2x%2B1%29=11-2x\"$ , squaring both sides we get:\r
\n" ); document.write( "\n" ); document.write( " $\"2x%5E2%2B2x%2B1=121-44x%2B4x%5E2\"$ , set the equation to zero: $\"2x%5E2-46x%2B120=0\"$ ,\r
\n" ); document.write( "\n" ); document.write( "divide both sides by 2 we get: $\"x%5E2-23x%2B60=0\"$ solving this equation by \r
\n" ); document.write( "\n" ); document.write( "factoring: $\"%28x-3%29%28x-20%29=0\"$ . The roots are x=3 and x=20. We reject the solution \r
\n" ); document.write( "\n" ); document.write( "x=20 because do not satisfy our problem.\r
\n" ); document.write( "\n" ); document.write( "Answer:The lengths are: 3m, 4m, 5m. \n" ); document.write( "

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