document.write( "Question 884695: The area of right angle triangle is 30cm2 and the length of its hypotenuse is 13 cm. the length of the shorter leg is: \n" ); document.write( "

Algebra.Com's Answer #534578 by Fombitz(32388) $\"\"$ $\"About$

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$\"%281%2F2%29AB=30\"$
\n" ); document.write( " $\"AB=60\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"A%5E2%2BB%5E2=13%5E2\"$
\n" ); document.write( " $\"A%5E2%2BB%5E2=169\"$
\n" ); document.write( "From the first equation,
\n" ); document.write( " $\"A=60%2FB\"$
\n" ); document.write( "Substitute,
\n" ); document.write( " $\"%2860%2FB%29%5E2%2BB%5E2=169\"$
\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( " $\"%28B%5E2-17B%2B60%29%28B%5E2%2B17B%2B60%29=0\"$
\n" ); document.write( " $\"%28B-5%29%28B-12%29%28B%2B5%29%28B%2B12%29=0\"$
\n" ); document.write( "Only the positive solution works here.
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"B-5=0\"$
\n" ); document.write( " $\"B=5\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"A=60%2F5\"$
\n" ); document.write( " $\"A=12\"$
\n" ); document.write( "and
\n" ); document.write( " $\"B-12=0\"$
\n" ); document.write( " $\"B=12\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"A=60%2F12\"$
\n" ); document.write( " $\"A=5\"$
\n" ); document.write( " \n" ); document.write( "

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