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

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) (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:
.
The problem tells us the area of the border is 330m^2.
Eq.1:
The area of the park = length * width.
Eq.2:
The problem tells us "the entire park is 5m longer than it is wide", which means: . Plugging that into Eq.2:
Eq. 3:
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= (because you subtract 2.5 from each end of the length)
Lawn width= (same reason).
So, , but we know , therefore:

Eq. 4:
---------
Now, we have enough to solve for w by plugging Eq. 4 and Eq. 3 into Eq. 1:

Let's solve this

----
The problem asks for the area of the lawn. Eq. 4 gives us the area of the lawn, so let's use that:

RELATED QUESTIONS
A small city park consists of a rectangular lawn surrounded on all sides by a... (answered by mananth)

A small city park consists of a rectangular lawn surrounded on all sides by a 330m sq.... (answered by hayek,ankor@dixie-net.com)

A small city park consists of a rectangular lawn surrounded on all sides by 330 meters... (answered by ankor@dixie-net.com)

I really need help on this problem please. A smal city park consists of a rectangular... (answered by KnightOwlTutor)

I do not understand how to set this problem up. A small city park consists of a... (answered by stanbon)

I have been struggling on this math problem for awhile now and I was wondering if anyone... (answered by stanbon)

Help!! I have a test on Friday and do not understand how to do this type of problem.... (answered by edjones)

A grass-plot, 18 yards long and 12 wide, is surrounded by a border of flowers of a... (answered by josgarithmetic)

A small rectangular playground that is 10 feet by 14 feet is going to have a grass border (answered by checkley77)