document.write( "Question 153515: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? \n" ); document.write( "
Algebra.Com's Answer #113036 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet?
\n" ); document.write( ":
\n" ); document.write( "Let x = width of the gravel path
\n" ); document.write( ":
\n" ); document.write( "Draw rough diagram of this labeling the garden as 18 by 13 and the width of the gravel path as x.
\n" ); document.write( "You will see the overall dimensions will be (2x+18) by (2x+13)
\n" ); document.write( ":
\n" ); document.write( "Overall area - garden area = gravel path area (required to be 516 sq/ft)
\n" ); document.write( "[(2x+18)(2x+13)] - (18*13) = 516
\n" ); document.write( ":
\n" ); document.write( "4x^2 + 62x + 234 - 234 = 516
\n" ); document.write( ";
\n" ); document.write( "4x^2 + 62x - 516 = 0
\n" ); document.write( "Simplify, divide equation by 2:
\n" ); document.write( "2x^2 + 31x - 258 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(2x + 43)(x - 6) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "x = +6 ft is the width of the gravel path
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution: (overall = 30 by 25, added 12 ft)
\n" ); document.write( "(30*25) - (18*13) =
\n" ); document.write( "750 - 234 = 516; confirms our solution \n" ); document.write( "
\n" );