SOLUTION: A small city park consists of a rectangular lawn surrounded on all sides by a 330m sq. border of flowers 2.5m wide. Find the area of the lawn if the entire park is 5m longer than

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Question 58191: A small city park consists of a rectangular lawn surrounded on all sides by a 330m sq. border of flowers 2.5m wide. Find the area of the lawn if the entire park is 5m longer than it is wide.
Found 2 solutions by hayek, ankor@dixie-net.com:
Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
Diagram
The border area is the area of the total park - the area of the lawn:
A%5Bb%5D=A%5Bp%5D-A%5Bl%5D.
The problem tells us the area of the border is 330m^2.
Eq.1: highlight%28330=A%5Bp%5D-A%5Bl%5D%29
The area of the park = length * width.
Eq.2: A%5Bp%5D=l%2Aw
The problem tells us "the entire park is 5m longer than it is wide", which means: green%28l=w%2B5%29. Plugging that into Eq.2:
Eq. 3: highlight%28A%5Bp%5D=%28w%2B5%29%2Aw%29
Finally, from the diagram, you should be able to see that the area of the lawn is the area of a rectangle having the following dimensions:
Lawn length=l-5 (because you subtract 2.5 from each end of the length)
Lawn width=w-5 (same reason).
So, A%5Bl%5D=%28l-5%29%2A%28w-5%29, but we know l=w%2B5, therefore:
A%5Bl%5D=%28w%2B5-5%29%28w-5%29
Eq. 4: A%5Bl%5D=highlight%28w%2A%28w-5%29%29
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Now, we have enough to solve for w by plugging Eq. 4 and Eq. 3 into Eq. 1:
330=%28%28w%2B5%29%2Aw%29-%28w%28w-5%29%29
Let's solve this
330=w%5E2%2B5w-%28w%5E2-5w%29
330=w%5E2%2B5w-w%5E2%2B5w
330=10w
highlight%28w=33%29
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The problem asks for the area of the lawn. Eq. 4 gives us the area of the lawn, so let's use that:
A%5Bl%5D=%2833%29%2833-5%29
highlight%28A%5Bl%5D=924m%5E2%29



Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A small city park consists of a rectangular lawn surrounded on all sides by a 330m sq. border of flowers 2.5m wide. Find the area of the lawn if the entire park is 5m longer than it is wide.
:
I assume they mean the area of the border is 330 sq ft
:
Let x = length of the park; (x-5) = the width of the park
:
Divide the walkway into 4 narrow rectangles:
2 ea: (x - 2.5) by 2.5
2 ea: (x - 7.5) by 2.5
:
The area equation:
2[(x-2.5)*2.5] + 2[(x-7.5)*2.5] = 330
2(2.5x - 6.25) + 2(2.5x - 18.75) = 330
5x - 12.5 + 5x - 37.5 = 330
10x - 50 = 330
10x = 330 + 50
10x = 380
x = 38 ft is the length, the width = 33 ft
:
Find the area of the entire park: 38*33 = 1254 sq ft.
Area of the lawn = 1254 - 330 = 924 sq ft.
:
Check it by finding the dimensions of the lawn and finding the area from that:
Lawn dimensions: (38-5) by (33-5): 33 * 28 = 924 sq ft also