document.write( "Question 202689: A rectangular patio is 7 ft longer than it is wide. Determine the dimensions of the patio if it measures 13 ft diagonally. Please solve involving applications of polynomials. \n" ); document.write( "
Algebra.Com's Answer #152884 by nerdybill(7384)\"\" \"About 
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A rectangular patio is 7 ft longer than it is wide. Determine the dimensions of the patio if it measures 13 ft diagonally. Please solve involving applications of polynomials.
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\n" ); document.write( "Let w = width of rectangle
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\n" ); document.write( "w+7 = length of rectangle
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\n" ); document.write( "From Pythagorean theorem we have:
\n" ); document.write( "w^2 + (w+7)^2 = 13^2
\n" ); document.write( "w^2 + (w+7)(w+7) = 13^2
\n" ); document.write( "w^2 + (w^2+7w+7w+49) = 169
\n" ); document.write( "2w^2+14w+49 = 169
\n" ); document.write( "2w^2+14w-120 = 0
\n" ); document.write( "w^2+7w-60 = 0
\n" ); document.write( "(w-5)(w+12) = 0
\n" ); document.write( "w = {5, -12}
\n" ); document.write( "We cam throw out the negative solution leaving:
\n" ); document.write( "w = 5 feet(width)
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\n" ); document.write( "length:
\n" ); document.write( "w+7 = 5+7 = 12 feet (length)
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\n" ); document.write( "Dimensions of rectangle: 5x7 feet \n" ); document.write( "
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