The perimeter of a rectangle is 36m. if its length is increased by 1m and the width is increased by 2m, its area will increase by 30m2. find the area of the original rectangle.

Let x and y be the dimension of the rectangle. Suppose x is the width and y is the length. Since the perimeter is 36, we have

If we increase the length by 1, we change . Similarly, if the width is increased by 2, we change . So, the increased area is

If we substitute the value for y deduced in the first equation, we have

The solutions to this equation are

One of them is negative, so we have to choose the positive one:

Which implies

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