A rectangular lawn is 40m wide and 60 m long. Stuart mows all the way along the perimeter of the lawn, leaving only 1,500 square meters to be mowed in the center of the lawn. How wide is the strip of lawn that Stuart has already mowed?
try making a drawing to start with...
it will look like two rectangles one inside another
what are the dimensions of the inner rectangle?
tell us how would you approach it?
area of given lawn (rectangle) = 40 x 60 = 2400 square metres
Suppose the width of the strip is w (in meters). The area of the strip Stuart mows is 2(60w + (40 - 2w)w) = 200w - 4w2 (we have to subtract the "corners" that the mower goes over twice).
This gives us: 2400 - 200w + 4w2 = 1500. Now let algebra work its magic (one solution won't work...why?).