document.write( "Question 165934: The legs of a right triangle differ by 2 centimeters and the hypotenuse is 4 centimeters more than the shorter leg. Find the sides of the triangle. \n" ); document.write( "

Algebra.Com's Answer #122289 by jojo14344(1513) $\"\"$ $\"About$

You can put this solution on YOUR website!
\n" ); document.write( " $\"shorter_leg=x\"$ ---> let's point it as the adjacent side
\n" ); document.write( " $\"x%2B2\"$ -------------> let's point it as the oppposite side
\n" ); document.write( " $\"x%2B4\"$ -------------> hypotenuse side
\n" ); document.write( "differ by 2cm -- $\"system%28x=adj%2Cx%2B2=opp%29\"$
\n" ); document.write( "By Pyth. Theorem:
\n" ); document.write( " $\"%28x%2B4%29%5E2=x%5E2%2B%28x%2B2%29%5E2\"$
\n" ); document.write( " $\"x%5E2%2B8x%2B16=x%5E2%2Bx%5E2%2B4x%2B4\"$
\n" ); document.write( " $\"2x%5E2%2B4x%2B4-x%5E2-8x-16=0\"$
\n" ); document.write( " $\"x%5E2-4x-12=0\"$ , perfect square, factorable
\n" ); document.write( " $\"%28x-6%29%28x%2B2%29=0\"$
\n" ); document.write( "2 values --- $\"system%28highlight%28x=6%29%2Cx=-2%29\"$
\n" ); document.write( "As highlighted, shortest side: adj= 6cm; opp=6+2=8cm; hyp=6+4=10cm
\n" ); document.write( "See below,
\n" ); document.write( "

$\"system%28green=adjacent=6cm%2Cblue=opposite=8cm%2Cred=hypotenuse=10cm%29\"$
\n" ); document.write( "check:
\n" ); document.write( " $\"10%5E2=6%5E2%2B8%5E2\"$
\n" ); document.write( " $\"100=36%2B64\"$
\n" ); document.write( " $\"100=100\"$
\n" ); document.write( "Thank you,
\n" ); document.write( "Jojo
\n" ); document.write( " \n" ); document.write( "

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