how would I find the solution to the following question:

A building measuring 90 m by 60 m is to be built. A paved area of uniform width will surround the building. The paved area is to have an area of 9000 m/s^2. How wide is the paved area?

Ok, imagine a rectangle inside of a rectangle. If we know the length of the sides of the small one, it is not hard to calculate the length of the large one.

Lets look at the long side of the big rectangle. For it to cover the small rectangle it would have to be larger than 90m. In fact if you draw lines from the small to the large that equal 90m you end up with

90m+two unknown lengths

If we do the same for the 60m side we get

60m+two unknown lengths

Since the paved area is uniform, the unknown lengths are equal to each other and form squares in the corner of your drawing. Lets call this length x.

Finally for the answer, the width of the paved part can be calculated by

base times height of large rectangle - base times height of small rectangle

(90+2x)(60+2x)-(60)(90)=9000

Where x is the distance from the small to the large. Solve for x and you have your answer!