document.write( "Question 1142615: The hypotenuse of a right triangle is 3 cm longer than the longer leg. The shorter leg is 21 cm shorter than the longer leg. Find the length of the longer leg of the triangle. \n" ); document.write( "

Algebra.Com's Answer #763346 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x be the length of the longer leg, in centimeters.\r\n" );
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document.write( "Then the shorter leg length is (x-21) cm, while the hypotenuse length is (x+3) cm.\r\n" );
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document.write( "The Pythagorean theorem gives you an equation\r\n" );
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document.write( "    x^2 + (x-21)^2 = (x+3)^2\r\n" );
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document.write( "Simplify and solve for x:\r\n" );
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document.write( "    x^2 + x^2 - 42x + 441 = x^2 + 6x + 9\r\n" );
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document.write( "    x^2 - 48x + 432 = 0\r\n" );
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document.write( "    (x-12)*(x-36) = 0\r\n" );
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document.write( "The roots of the last equation are 12 and 36.\r\n" );
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document.write( "But only greater of the two roots, namely 36, is the solution to the problem,\r\n" );
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document.write( "since 12 becomes NEGATIVE, when 21 is subtracted from it.\r\n" );
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document.write( "ANSWER.  The longer leg is 36 cm long.\r\n" );
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document.write( "CHECK.   36^2 + (36-21)^2 = 1521,  and  (36+3)^2 = 39^2 = 1521.    ! Correct !\r\n" );
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