document.write( "Question 1200784: The hypotenuse of a right triangle is 4 cm. longer than one leg and 8 cm. longer than the other leg. Solve for the sides using the Pythagorean theorem. \n" ); document.write( "

Algebra.Com's Answer #834987 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x be the longest leg.\r\n" );
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document.write( "Then the shortest leg is (x-4) and the hypotenuse is (x+4).\r\n" );
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document.write( "Write the Pythagoras equation\r\n" );
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document.write( "    (x-4)^2 + x^2 = (x+4)^2\r\n" );
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document.write( "    (x^2 - 8x + 16) + x^2 = x^2 + 8x + 16\r\n" );
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document.write( "     2x^2 = 16x \r\n" );
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document.write( "     x*(x-8) = 0.\r\n" );
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document.write( "The roots are x= 0 and/or x= 8.  Obviously, only positive root x= 8 is the solution to the problem.\r\n" );
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document.write( "ANSWER.  The legs are 4 cm and 8 cm; the hypotenuse is 12 cm.\r\n" );
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document.write( "Alternatively, the problem can be solved mentally, by noticing that this right-angled triangle\r\n" );
document.write( "is a standard (3,4,5) Pythagorean triangle.\r\n" );
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