document.write( "Question 846776: The sides of a right triangle have lengths (x-5), (x+2), and (x+3). Find the value of x and the length of each side. \n" ); document.write( "

Algebra.Com's Answer #510011 by Fombitz(32388) $\"\"$ $\"About$

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Use the Pythagorean theorem,
\n" ); document.write( " $\"%28x%2B3%29%5E2=%28x-5%29%5E2%2B%28x%2B2%29%5E2\"$
\n" ); document.write( " $\"x%5E2%2B6x%2B9=x%5E2-10x%2B25%2Bx%5E2%2B4x%2B4\"$
\n" ); document.write( " $\"x%5E2%2B6x%2B9=2x%5E2-6x%2B29\"$
\n" ); document.write( " $\"x%5E2-12x%2B20=0\"$
\n" ); document.write( " $\"%28x-2%29%28x-10%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x-2=0\"$
\n" ); document.write( " $\"x=2\"$
\n" ); document.write( "The sides would then be -3,0,and 5.
\n" ); document.write( "This is not a good solution.
\n" ); document.write( " $\"x-10=0\"$
\n" ); document.write( " $\"x=10\"$
\n" ); document.write( "The sides would then be 5,12,and 13.
\n" ); document.write( "This is a good solution. \n" ); document.write( "

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