document.write( "Question 78375: Geometry. The length of one leg of a right triangle is 3in. more than the other. If the length of the hypotenuse is 15 in., what are the lengths of the two legs? \n" ); document.write( "
Algebra.Com's Answer #56204 by dolly(163)\"\" \"About 
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Let the length of 1 leg = x in
\n" ); document.write( "So the length of the other leg = (x + 3) in\r
\n" ); document.write( "\n" ); document.write( "Then by Pythagorean theorem, the hypotenuse is given by,\r
\n" ); document.write( "\n" ); document.write( "x^2 + (x+3)^2 = hyp^2
\n" ); document.write( "==> x^2 + (x+3)^2 = 15^2
\n" ); document.write( "==> x^2 + x^2 + 6x + 9 = 225 [expanding (x+3)^2 using identity]
\n" ); document.write( "==> 2x^2 + 6x + 9 = 225
\n" ); document.write( "==> 2x^2 + 6x + 9 - 225 = 0
\n" ); document.write( "==> 2x^2 + 6x - 216 = 0
\n" ); document.write( "==> x^2 + 3x - 108 = 0 [dividing by 2 throughout]
\n" ); document.write( "==> x^2 + 12x - 9x - 108 = 0
\n" ); document.write( "==> x(x+ 12) - 9(x+12) = 0
\n" ); document.write( "==> (x+12)(x-9) = 0
\n" ); document.write( "==> x+12 = 0 or x - 9 = 0
\n" ); document.write( "==> x = -12 or x = 9
\n" ); document.write( "As length cannot be negative, x = 9
\n" ); document.write( "==> one length of the triangle = 9 in
\n" ); document.write( "The other leg measures = 9+3
\n" ); document.write( " = 12 in\r
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