document.write( "Question 340309: If (6-x), (13-x), and (14-x) are the lengths of the sides of a right triangle, find the value of x. \n" ); document.write( "

Algebra.Com's Answer #243824 by J2R2R(94) $\"\"$ $\"About$

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We have three sides 6 - x, 13 - x, 14 - x\r
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\n" ); document.write( "\n" ); document.write( "14 - x is the largest so this must be the hypotenuse.\r
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\n" ); document.write( "\n" ); document.write( "Therefore using Pythagoras we have\r
\n" ); document.write( "\n" ); document.write( "(6 - x)^2 + (13 - x)^2 = (14 - x)^2\r
\n" ); document.write( "\n" ); document.write( "36 - 12x + x^2 + 169 - 26x + x^2 = 196 - 28x + x^2\r
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\n" ); document.write( "\n" ); document.write( "which gives:\r
\n" ); document.write( "\n" ); document.write( "x^2 - 10x + 9 = 0\r
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\n" ); document.write( "\n" ); document.write( "Factorising gives (x - 1)(x - 9) = 0\r
\n" ); document.write( "\n" ); document.write( "x = 1 and x = 9 give solutions to the equation.\r
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\n" ); document.write( "\n" ); document.write( "With x = 1 we have sides 5, 12 and 13 which is reasonable; but with x = 9 we have sides -3, 4 and 5 which does satisfy the equation but as we are talking about lengths (which are all positive) we disregard this answer.\r
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\n" ); document.write( "\n" ); document.write( "Therefore the sides are 5, 12 and 13 with x = 1. \n" ); document.write( "

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