document.write( "Question 195253: the perimeter of the quadrilateral is 130 inches. Find the lengths of the sides. The given sides are x+2, 2x+1, x-5, x^2-3x.

Algebra.Com's Answer #146447 by windsolace(8)

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A quadrilateral has 4 sides as suggested in the name (quad). Add up the 4 sides given in the question.\r
\n" ); document.write( "\n" ); document.write( "(x+2) + (2x+1) + (x-5) + (x^2-3x)\r
\n" ); document.write( "\n" ); document.write( "It is given in the question that the perimeter is 130 inches. Hence:\r
\n" ); document.write( "\n" ); document.write( "(x+2) + (2x+1) + (x-5) + (x^2-3x) = 130 \r
\n" ); document.write( "\n" ); document.write( "Simplify the equation:\r
\n" ); document.write( "\n" ); document.write( "x^2 - x - 2 = 130\r
\n" ); document.write( "\n" ); document.write( "x^2 - x - 132 = 0 \r
\n" ); document.write( "\n" ); document.write( "By factorisation:\r
\n" ); document.write( "\n" ); document.write( "(x - 12)( x + 11)= 0\r
\n" ); document.write( "\n" ); document.write( "Therefore x = 12 or x = - 11 (reject since x cannot be negative)\r
\n" ); document.write( "\n" ); document.write( "Substitute x = 12 into the 4 sides given: \r
\n" ); document.write( "\n" ); document.write( "x + 2 = 12 + 2 = 14
\n" ); document.write( "2x + 1 = 2(12) + 1 = 25
\n" ); document.write( "x - 5 = 12 - 5 = 7
\n" ); document.write( "x^2 - 3x = (12)^2 - 3(12) = 108\r
\n" ); document.write( "\n" ); document.write( "Hence, the 4 sides of the quadrilateral are 14 inches, 25 inches , 7 inches and 108 inches.
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