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?

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- September 5th 2013, 09:17 PMHell0Oh, Stuart
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?

- September 5th 2013, 09:29 PMADARSHRe: Oh, Stuart
try making a drawing to start with...

it will look like two rectangles one inside another

what are the dimensions of the inner rectangle?

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tell us how would you approach it?

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area of given lawn (rectangle) = 40 x 60 = 2400 square metres - September 5th 2013, 10:45 PMDevenoRe: Oh, Stuart
Some thoughts:

Suppose the width of the strip is w (in meters). The area of the strip Stuart mows is 2(60w + (40 - 2w)w) = 200w - 4w^{2}(we have to subtract the "corners" that the mower goes over twice).

This gives us: 2400 - 200w + 4w^{2}= 1500. Now let algebra work its magic (one solution won't work...why?).