document.write( "Question 351080: the area of a right angle triangle is 30 sq. cm and the length of the hypotenuse is 13 sq. cm. the length of the shorter side is?
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Algebra.Com's Answer #250969 by Fombitz(32388) $\"\"$ $\"About$

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From the Pythagorean theorem,
\n" ); document.write( " $\"A%5E2%2BB%5E2=13%5E2\"$
\n" ); document.write( "From the area,
\n" ); document.write( " $\"%281%2F2%29AB=30\"$
\n" ); document.write( " $\"%281%2F4%29A%5E2B%5E2=900\"$
\n" ); document.write( " $\"A%5E2=3600%2FB%5E2\"$
\n" ); document.write( "Substitute,
\n" ); document.write( " $\"3600%2FB%5E2%2BB%5E2=169\"$
\n" ); document.write( " $\"3600%2BB%5E4=169B%5E2\"$
\n" ); document.write( " $\"B%5E4-169B%5E2%2B3600=0\"$
\n" ); document.write( " $\"%28B%5E2-144%29%28B%5E2-25%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"B%5E2=144\"$
\n" ); document.write( " $\"A%5E2=25\"$
\n" ); document.write( " $\"B=12\"$
\n" ); document.write( " $\"A=5\"$
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\n" ); document.write( ".
\n" ); document.write( " $\"B%5E2=25\"$
\n" ); document.write( " $\"A%5E2=144\"$
\n" ); document.write( " $\"B=5\"$
\n" ); document.write( " $\"A=12\"$
\n" ); document.write( "The shorter leg is 5 cm.
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