document.write( "Question 78361: Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path? \n" ); document.write( "
Algebra.Com's Answer #56212 by ankor@dixie-net.com(22740)\"\" \"About 
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A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path?
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\n" ); document.write( "draw this as a 30 by 20 rectangle with a uniform path. Label the width of this
\n" ); document.write( "path as x. It becomes apparent that the dimensions inside the path, which is given
\n" ); document.write( "as 400 sq ft, is (30-2x) by 20-2x).
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\n" ); document.write( "(30-2x) * (20-2x) = 400
\n" ); document.write( "600 - 100x + 4x^2 = 400
\n" ); document.write( "600 - 400 - 100x + 4x^2 = 0; subtracted 400 from both sides
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\n" ); document.write( "Arrange as a quadratic equation:
\n" ); document.write( "4x^2 - 100x + 200 = 0
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\n" ); document.write( "Simplify, divide equation by 4:
\n" ); document.write( "x^2 - 25x + 50 = 0
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\n" ); document.write( "Use the quadratic formula so find x: a=1; b=-25; c=50
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\n" ); document.write( "only one of the solutions will make sense. I got ~ 2.2 ft
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\n" ); document.write( "Check it:
\n" ); document.write( "(30-4.4) * (20-4.4) =
\n" ); document.write( " 25.6 * 15.6 = 399.36 ~ 400, confirms our solution
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