document.write( "Question 847742: If the longest side of a right triangle is 13 and the perimeter is 30 what is the shortest side? \n" ); document.write( "

Algebra.Com's Answer #510670 by Fombitz(32388) $\"\"$ $\"About$

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For this right triangle,
\n" ); document.write( "1. $\"A%5E2%2BB%5E2=13%5E2\"$
\n" ); document.write( "and
\n" ); document.write( " $\"A%2BB%2B13=30\"$
\n" ); document.write( "2. $\"A%2BB=17\"$
\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"A=17-B\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"%2817-B%29%5E2%2BB%5E2=169\"$
\n" ); document.write( " $\"289-34B%2BB%5E2%2BB%5E2=169\"$
\n" ); document.write( " $\"2B%5E2-34B%2B120=0\"$
\n" ); document.write( " $\"B%5E2-17B%2B60=0\"$
\n" ); document.write( " $\"%28B-5%29%28B-12%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"B-5=0\"$
\n" ); document.write( " $\"B=5\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"A=17-5=12\"$
\n" ); document.write( "and
\n" ); document.write( " $\"B-12=0\"$
\n" ); document.write( " $\"B=12\"$
\n" ); document.write( "then
\n" ); document.write( " $\"A=17-12=5\"$ \n" ); document.write( "

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