document.write( "Question 277296: The area of a rectangle is 32 square inches. The length is 4 inches longer than the width. What is the length? What is the width? What is the perimeter? \n" ); document.write( "

Algebra.Com's Answer #201924 by oberobic(2304) $\"\"$ $\"About$

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The area of a rectangle = length * width = l * w = 32 sq inches
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\n" ); document.write( "l = w + 4 :: given
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\n" ); document.write( "substituting
\n" ); document.write( "(w+4) * w = 32
\n" ); document.write( "w^2 + 4w = 32
\n" ); document.write( "w^2 + 4w - 32 = 0
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\n" ); document.write( "factoring
\n" ); document.write( "(w+8)(w-4) = 0
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\n" ); document.write( "so the solutions are w=-8 and w=4.
\n" ); document.write( "of course, a negative length is nonsense, so the only answer appears to be w=4
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\n" ); document.write( "given l = w+4, then l= 4+4 = 8
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\n" ); document.write( "checking the area
\n" ); document.write( "4*8 = 32??
\n" ); document.write( "yes
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\n" ); document.write( "the perimeter of a rectangle = 2l + 2w = 2(8) + 2(4) = 16+8 = 24
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\n" ); document.write( "Answer:
\n" ); document.write( "Length = 8
\n" ); document.write( "Width = 4
\n" ); document.write( "Perimeter = 24
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\n" ); document.write( "done \n" ); document.write( "

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