SOLUTION: A rectangular garden is twice as long as it is wide and is surrounded by a sidewalk, that is 4 ft wide. The area of the sidewalk is 256 ft2. Find the dimensions of the garden.

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Question 626847: A rectangular garden is twice as long as it is wide and is surrounded by a sidewalk, that is 4 ft wide. The area of the sidewalk is 256 ft2. Find the dimensions of the garden.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the width of the garden (in feet).
Since the garden is twice as long as it is wide,
its length must be 2x.
With one piece of sidewalk on each side,
the dimensions (in feet) of the garden plus sidewalk are
width=x%2B4%2B4=x%2B8 and
length=2x%2B4%2B4=2x%2B8
It would look like this:

The area (in square feet) of the whole thing is
length%2Awidth=%282x%2B8%29%28x%2B8%29=2x%5E2%2B16x%2B8x%2B64=2x%5E2%2B24x%2B64
The area of the garden part only is
%282x%29%28x%29=2x%5E2
The difference is the area (in square feet) of the sidewalk only,
2x%5E2%2B24x%2B64-2x%5E2=256 --> 24x%2B64=256
Subtracting 64 from both sides of the equal sign we get
24x%2B64=256 --> 24x%2B64-64=256-64 --> 24x=192
Dividing both sides of the equal sign by 24 we get
24x=192 --> 24x%2F24=192%2F24 --> highlight%28x=8%29
The garden is highlight%288%29 feet wide, and 2x=2%2A8=highlight%2816%29 feet long