document.write( "Question 1140065: The dimensions of a rectangular garden are 5m x 8m. There is a path around the garden of uniform width that is the same area as the garden. What are the dimensions of the backyard? (DRAW PICTURE)
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Algebra.Com's Answer #760526 by KMST(5328) $\"\"$ $\"About$

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The garden is a rectangle with area $\"%285m%29%2A%288m%29=40\"$ $\"m%5E2\"$ .
\n" ); document.write( "A path of width $\"x%2F2\"$ $\"m\"$ around that garden would add $\"x\"$ $\"m\"$ to the length and $\"x\"$ $\"m\"$ to the width of that rectangle. The garden plus the path would form a larger rectangle with length $\"8%2Bx\"$ $\"m\"$ and width $\"5%2Bx\"$ $\"m\"$ . The area of that larger rectangle would be double the area of the garden: $\"2%2840m%5E2%29=80m%5E2\"$ .
\n" ); document.write( "So $\"%28x%2B8%29%2A%28x%2B5%29=80\"$ .
\n" ); document.write( " $\"x%5E2%2B13x%2B40=80\"$
\n" ); document.write( " $\"x%5E2%2B13x-40=0\"$ or $\"x%5E2%2B13x=40\"$
\n" ); document.write( "That equation can be solved by completing the square, or applying the quadratic formula to find as solutions
\n" ); document.write( " $\"x=%28-13+%2B-+sqrt%28329%29%29%2F2\"$ .
\n" ); document.write( "As we were adding a length $\"x%3E0\"$ to the width and length of the garden,
\n" ); document.write( "the only applicable answer is
\n" ); document.write( " $\"x=%28-13+%2B+sqrt%28329%29%29%2F2=sqrt%28329%29%2F2-6.5=about2.569\"$ (making $\"x%2F2=about1.286m\"$ .
\n" ); document.write( "Adding that to the garden's dimensions,
\n" ); document.write( "he width (in m) of garden plus path would be
\n" ); document.write( " $\"5-6.5+%2B+sqrt%28329%29%2F2=sqrt%28329%29%2F2%7D-1.5=about7.57\"$ ,
\n" ); document.write( "and the length (in m) of the garden plus path would be
\n" ); document.write( " $\"8%2B+sqrt%28329%29%2F2-6.5=sqrt%28329%29%2F2%7D%2B1.5=about10.57\"$ .
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\n" ); document.write( "Is there anything else in that backyard? A pool? A patio? A chicken coop? A stream?
\n" ); document.write( "If the backyard is only the garden and the path of uniform width around it, with the same area as the garden, then the backyard's dimensions are as stated above \n" ); document.write( "

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