document.write( "Question 190807: A rectangular garden is 12 feet by 5 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 square feet? \n" ); document.write( "

Algebra.Com's Answer #143265 by orca(409) $\"\"$ $\"About$

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Let x be the width of the path.
\n" ); document.write( "Then the dimensions of the rectangle formed by the outer edges of the path can is:
\n" ); document.write( "Length: 2x + 12
\n" ); document.write( "Width: 2x + 5
\n" ); document.write( "So its area = (2x+12)(2x + 5) = 2(x +6)(2x+5)\r
\n" ); document.write( "\n" ); document.write( "The area of the garden is 12x5\r
\n" ); document.write( "\n" ); document.write( "Therefore the area of the gravel path = 2(x+6)(2x+5)-12x5
\n" ); document.write( "Setting the area of the gravel path equal to 138, we have
\n" ); document.write( "2(x+6)(2x+5)-12x5 = 138\r
\n" ); document.write( "\n" ); document.write( "Dividing both sides by 2 to simplify it, we have
\n" ); document.write( "(x+6)(2x+5)-6x5 = 69\r
\n" ); document.write( "\n" ); document.write( "Solving the equation for x, we have
\n" ); document.write( " $\"2x%5E2+%2B17x%2B30-30=69\"$
\n" ); document.write( " $\"2x%5E2+%2B17x-69=0\"$
\n" ); document.write( "Then solve the equation for x using the quadratic formula.\r
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