document.write( "Question 1170475: the lengths of the sides of a right triangle are given by three consecutive integers. find the lengths of all three sides \n" ); document.write( "

Algebra.Com's Answer #795350 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "if we have $\"n+\"$ as the first integer, then $\"n%2B1+\"$ will be the second integer, $\"+n%2B2\"$ will be the third integer\r
\n" ); document.write( "\n" ); document.write( "the lengths of the sides of a $\"right\"$ $\"+triangle\"$ are given by three consecutive integers so that
\n" ); document.write( " $\"n+\"$ and $\"n%2B1+\"$ are legs
\n" ); document.write( " $\"+n%2B2\"$ hypothenuse\r
\n" ); document.write( "\n" ); document.write( " $\"+%28n%2B2%29%5E2=n%5E2%2B%28n%2B1%29%5E2\"$ .......solve for $\"n+\"$
\n" ); document.write( " $\"+n%5E2%2B4n%2B4=n%5E2%2Bn%5E2%2B2n%2B1\"$
\n" ); document.write( " $\"+n%5E2%2B4n%2B4=2n%5E2%2B2n%2B1\"$
\n" ); document.write( " $\"+0=2n%5E2-n%5E2-4n%2B2n%2B1-4\"$
\n" ); document.write( " $\"+0=n%5E2-2n-3\"$
\n" ); document.write( " $\"+0=n%5E2%2Bn-3n-3\"$
\n" ); document.write( " $\"+0=%28n%5E2%2Bn%29-%283n%2B3%29\"$
\n" ); document.write( " $\"+0=n%28n%2B1%29-3%28n%2B1%29\"$
\n" ); document.write( " $\"+0=%28n-3%29%28n%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions:
\n" ); document.write( " $\"n=3\"$
\n" ); document.write( " $\"n=-1\"$ ...disregard negative solution\r
\n" ); document.write( "\n" ); document.write( "the lengths of all three sides:
\n" ); document.write( " $\"3\"$ , $\"4+\"$ , and $\"+5\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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