Math CentralQuandaries & Queries


Question from Charlene, a student:

The area of a rectangle is 390m^2. If its length is increased by 10m and its width is decreased by 6m, then its area does not change. Find the perimeter of the original rectangle.


Let  x  be the length, and  y  be the width of the rectangle.
The area and perimeter of the rectangle are:

Area = x · y       Perimeter = 2x + 2y

We are given that the area is 390 metres square and remains the same if the length is increased by 10 and the width decreased by 6, thus:

x · y = 390     (x + 10)(y - 6) = 390


x · y = (x + 10)(y - 6)
x · y = x · y - 6x + 10y - 60
60 = - 6x + 10y
y = (60 + 6x)/10

And we have a value to substitute back into our first equation,

390 = x (60 + 6x)/10

Solve for  x  , and then for  y  , then determine perimeter.



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