SOLUTION: A rectangular flower garden is 8ft longer thant it is wide. It is surrounded by a brick walk 2ft wide. The area is 176ft^2. Find the dimensions. I know that the equation is set

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Question 389660: A rectangular flower garden is 8ft longer thant it is wide. It is surrounded by a brick walk 2ft wide. The area is 176ft^2. Find the dimensions.
I know that the equation is set = to 176 and that width = x and length = x+8 but I am missing what to do with the brick walk 2ft wide. Having problems setting problem up to solve. Would appreciate help!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = width of the garden. So because the "garden is 8ft longer thant it is wide", we know that the length of the garden is x%2B8


If you draw the picture, you should get




Note: we're adding 2 ft to each dimension twice because there are two red sides per dimension.


Edit: I'm assuming that the area of the brick ONLY is 176 square feet.


So we can see that the dimensions of the entire rectangle are x+4 by x+12. So the area of the entire thing is %28x%2B4%29%28x%2B12%29


Because the area of the garden only is x%28x%2B8%29, this means that the area of the brick ONLY is


%28x%2B4%29%28x%2B12%29-x%28x%2B8%29=176


Note: I'm subtracting the area of the garden from the area of the entire enclosure.


%28x%2B4%29%28x%2B12%29-x%28x%2B8%29=176 Start with the given equation.


x%5E2%2B16x%2B48-x%28x%2B8%29=176 FOIL


x%5E2%2B16x%2B48-x%5E2-8x=176 Distribute.


8x%2B48=176 Combine like terms.


8x=176-48 Subtract 48 from both sides.


8x=128 Combine like terms on the right side.


x=%28128%29%2F%288%29 Divide both sides by 8 to isolate x.


x=16 Reduce.


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Answer:

So the solution is x=16


This means that the width of the garden is 16 feet.


Now plug this into x%2B8 to get x%2B8=16%2B8=24


So the length of the garden is 24 feet.


So the garden alone is 16 x 24 ft


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim