SOLUTION: a small city park consists of a rectangler lawn surrounded on all sides by a 330 m squared border of flowers 2.5m wide. find the area of the lawn if the entire park is 5 m longe

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: a small city park consists of a rectangler lawn surrounded on all sides by a 330 m squared border of flowers 2.5m wide. find the area of the lawn if the entire park is 5 m longe      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 175195: a small city park consists of a rectangler lawn surrounded on all sides by a 330 m squared border of flowers 2.5m wide. find the area of the lawn if the entire park is 5 m longer than it is wide
Answer by Mathtut(3670) 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
---------
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
----
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