document.write( "Question 988686: Find the dimensions of a rectangle whose area is 182 cm2 and whose perimeter is 54 cm. (Enter your answers as a comma-separated list.) \n" ); document.write( "
Algebra.Com's Answer #609369 by ankor@dixie-net.com(22740)\"\" \"About 
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Find the dimensions of a rectangle whose area is 182 cm2 and whose perimeter is 54 cm. (Enter your answers as a comma-separated list.)
\n" ); document.write( "Let L = the length
\n" ); document.write( "Let W = the width
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\n" ); document.write( "The perimeter
\n" ); document.write( "2L + 2W = 54
\n" ); document.write( "simplify divide by 2
\n" ); document.write( "L + W = 27
\n" ); document.write( "W = (27-L), use this form for substitution
\n" ); document.write( ":
\n" ); document.write( "The area
\n" ); document.write( "L * W = 182
\n" ); document.write( "Replace W with (27-L)
\n" ); document.write( "L(27-L) = 182
\n" ); document.write( "27L - L^2 = 182
\n" ); document.write( "a quadratic equation
\n" ); document.write( "-L^2 + 27L - 182 = 0
\n" ); document.write( "Factor easier if we multiply by -1 and change the signs
\n" ); document.write( "L^2 - 27L + 182 = 0
\n" ); document.write( "you can use the quadratic formula here, but this will factor to
\n" ); document.write( "(L-14)(L-13) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "L = 14, W = 13
\n" ); document.write( "or
\n" ); document.write( "L = 13, W = 14
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this
\n" ); document.write( "2(14) + 2(13) = 54
\n" ); document.write( "14 * 13 = 182
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