document.write( "Question 150955: Use a system of equations to solve the word problem. The perimeter of a rectangle is 56 inches, and its area is 192 square inches. What are the dimensions? \n" ); document.write( "
Algebra.Com's Answer #110909 by nerdybill(7384)\"\" \"About 
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Use a system of equations to solve the word problem. The perimeter of a rectangle is 56 inches, and its area is 192 square inches. What are the dimensions?
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\n" ); document.write( "Let L = length of the rectangle
\n" ); document.write( "and W = width of the rectangle
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\n" ); document.write( "For a 'rectangle' we know the following:
\n" ); document.write( "perimeter = 2(L+W)
\n" ); document.write( "area = LW
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\n" ); document.write( "This then, allows us to derive our \"system of equations\":
\n" ); document.write( "56 = 2(L+W) (equation 1)
\n" ); document.write( "192 = LW (equation 2)
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\n" ); document.write( "Solving equation 2 for W we get:
\n" ); document.write( "192 = LW
\n" ); document.write( "192/L = W
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\n" ); document.write( "Substitute the above into equation 1 and solve for L:
\n" ); document.write( "56 = 2(L+W)
\n" ); document.write( "56 = 2(L + 192/L)
\n" ); document.write( "56L = 2(L^2 + 192)
\n" ); document.write( "28L = (L^2 + 192)
\n" ); document.write( "0 = L^2 - 28L + 192
\n" ); document.write( "Factoring:
\n" ); document.write( "0 = (L-16)(L-12)
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\n" ); document.write( "L = {16,12}
\n" ); document.write( "Therefore, the dimensions are:
\n" ); document.write( "12 inches by 16 inches\r
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