Question 58191
<img src="http://i13.tinypic.com/2cifr5k.jpg" border="0" alt="Diagram">
The border area is the area of the total park - the area of the lawn:
{{{A[b]=A[p]-A[l]}}}.

The problem tells us the area of the border is 330m^2.
Eq.1: {{{highlight(330=A[p]-A[l])}}}

The area of the park = length * width.
Eq.2: {{{A[p]=l*w}}}

The problem tells us "the entire park is 5m longer than it is wide", which means: {{{green(l=w+5)}}}.  Plugging that into Eq.2:
Eq. 3:  {{{highlight(A[p]=(w+5)*w)}}}

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[l]=(l-5)*(w-5)}}}, but we know {{{l=w+5}}}, therefore:
{{{A[l]=(w+5-5)(w-5)}}}
Eq. 4: {{{A[l]=highlight(w*(w-5))}}}
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Now, we have enough to solve for w by plugging Eq. 4 and Eq. 3 into Eq. 1:
{{{330=((w+5)*w)-(w(w-5))}}}
Let's solve this
{{{330=w^2+5w-(w^2-5w)}}}
{{{330=w^2+5w-w^2+5w}}}
{{{330=10w}}}
{{{highlight(w=33)}}}
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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[l]=(33)(33-5)}}}
{{{highlight(A[l]=924m^2)}}}