document.write( "Question 165568: one leg of a right triangle is 14 inches longer than the smaller leg, and the hypotenuse is 16 inch longer than the smaller leg. find the lengths of the sides of the triangle \n" ); document.write( "

Algebra.Com's Answer #122030 by josmiceli(19441) $\"\"$ $\"About$

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Call the smaller leg $\"x\"$
\n" ); document.write( "Call the hypotenuse $\"h\"$
\n" ); document.write( "The longer leg = $\"x%2B14\"$
\n" ); document.write( " $\"h+=+x+%2B+16\"$
\n" ); document.write( " $\"h%5E2+=+x%5E2+%2B+%28x%2B14%29%5E2\"$
\n" ); document.write( " $\"%28x%2B16%29%5E2+=+x%5E2+%2B+x%5E2+%2B+28x+%2B+196\"$
\n" ); document.write( " $\"x%5E2+%2B+32x+%2B+256+=+2x%5E2+%2B+28x+%2B+196\"$
\n" ); document.write( " $\"x%5E2+-+4x+-+60+=+0\"$
\n" ); document.write( "You can solve by completing the square
\n" ); document.write( " $\"x%5E2+-+4x+%2B+%284%2F2%29%5E2+=+60+%2B+%284%2F2%29%5E2\"$
\n" ); document.write( " $\"x%5E2+-+4x+%2B+4+=+64\"$
\n" ); document.write( " $\"%28x+-+2%29%5E2+=+8%5E2\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"x+-+2+=+8\"$
\n" ); document.write( " $\"x+=+10\"$
\n" ); document.write( " $\"x+%2B+14+=+24\"$
\n" ); document.write( " $\"x+%2B+16+=+26\"$
\n" ); document.write( "The sides are 10,24, and 26
\n" ); document.write( "check answer
\n" ); document.write( " $\"h%5E2+=+x%5E2+%2B+%28x%2B14%29%5E2\"$
\n" ); document.write( " $\"26%5E2+=+10%5E2+%2B+24%5E2\"$
\n" ); document.write( " $\"676+=+100+%2B+576\"$
\n" ); document.write( " $\"676+=+676\"$
\n" ); document.write( "OK \n" ); document.write( "

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