document.write( "Question 329105: The sides of right triangle are consecutive multiples of three. Find the length of the hypotenuse. \n" ); document.write( "

Algebra.Com's Answer #235823 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use the Pythagorean theorem,
\n" ); document.write( " $\"%283n%29%5E2%2B%283%28n%2B1%29%29%5E2=%283%28n%2B2%29%29%5E2\"$
\n" ); document.write( " $\"9n%5E2%2B9%28n%5E2%2B2n%2B1%29=9%28n%5E2%2B4n%2B4%29\"$
\n" ); document.write( " $\"2n%5E2%2B2n%2B1=n%5E2%2B4n%2B4\"$
\n" ); document.write( " $\"n%5E2-2n-3=0\"$
\n" ); document.write( " $\"%28n-3%29%28n%2B1%29=0\"$
\n" ); document.write( "Only the positive solution makes sense in this problem,
\n" ); document.write( " $\"n-3=0\"$
\n" ); document.write( " $\"n=3\"$
\n" ); document.write( "The hypotenuse is $\"3%28n%2B2%29=15\"$ . \n" ); document.write( "

\n" );