document.write( "Question 712636: I'm having trouble with this one! A rectangular garden has dimensions 3m by 4m. A path is built around the garden. The area of the garden and path is 6 times as great as the area of the garden. What is the width of the path? \n" ); document.write( "
Algebra.Com's Answer #438085 by nerdybill(7384)\"\" \"About 
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A rectangular garden has dimensions 3m by 4m. A path is built around the garden. The area of the garden and path is 6 times as great as the area of the garden. What is the width of the path?
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\n" ); document.write( "Let x = width (m) of path
\n" ); document.write( "then
\n" ); document.write( "area of \"path+garden\" = (2x+3)(2x+4)
\n" ); document.write( "area of \"garden\" = 3*4 = 12
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\n" ); document.write( "From:\"The area of the garden and path is 6 times as great as the area of the garden.\" we get our equation:
\n" ); document.write( "(2x+3)(2x+4) = 6*12
\n" ); document.write( "4x^2+8x+6x+12 = 72
\n" ); document.write( "4x^2+14x+12 = 72
\n" ); document.write( "4x^2+14x-60 = 0
\n" ); document.write( "2x^2+7x-30 = 0
\n" ); document.write( "rewrite middle term:
\n" ); document.write( "2x^2+12x-5x-30 = 0
\n" ); document.write( "group:
\n" ); document.write( "(2x^2+12x)-(5x+30) = 0
\n" ); document.write( "2x(x+6)- 5(x+6) = 0
\n" ); document.write( "(x+6)(2x-5) = 0
\n" ); document.write( "x = {-6, 5/2}
\n" ); document.write( "we can throw out the negative solution (extraneous) leaving:
\n" ); document.write( "x = 5/2
\n" ); document.write( "or
\n" ); document.write( "x = 2.5 m\r
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