document.write( "Question 276567: A rectangle has an area of 144cm^2 and a perimeter of 68cm. What are the lengths of the sides? \n" ); document.write( "

Algebra.Com's Answer #201528 by stanbon(75887) $\"\"$ $\"About$

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A rectangle has an area of 144cm^2 and a perimeter of 68cm. What are the lengths of the sides?
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\n" ); document.write( "Equations:
\n" ); document.write( "LW = 144
\n" ); document.write( "2(L+W) = 68
\n" ); document.write( "-----
\n" ); document.write( "LW = 144
\n" ); document.write( "L + W = 34
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\n" ); document.write( "L = 34-W
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\n" ); document.write( "Substitute and solve for \"W\":
\n" ); document.write( "(34-W)W = 144
\n" ); document.write( "-w^2 + 34w - 144 = 0
\n" ); document.write( "w^2 - 34w + 144 = 0
\n" ); document.write( "---
\n" ); document.write( "w = [34 +- sqrt(34^2 -4*144)]/2
\n" ); document.write( "----
\n" ); document.write( "w = [34 +- sqrt(580)]/2
\n" ); document.write( "Positive solution:
\n" ); document.write( "w = (17 + sqrt(145))
\n" ); document.write( "W is appoximately 29.04 cm
\n" ); document.write( "----
\n" ); document.write( "Since L + W = 34, L = 34-29.04 = 4.96 cm
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\n" ); document.write( "Cheers,
\n" ); document.write( "stan H. \n" ); document.write( "

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