The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 3. What was the size of the original rectangle?

Question

The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 3. What was the size of the original rectangle?

Answer 1

Let's assume the original width is w. Then the length must be w+10, and the area (length x width) = w (w+10).

If the sides are increased by 10, the new sides are w+10 and w+20, and the new area (w+10) (w+20).

This must be 3 times the original area ie 3w (w+10).

So (w+10) (w+20) = 3w (w+10).

If we assume w+10 is non-zero (which it must be as it is a side of our original rectangle) we can divide both sides of the equation by it.

This gives w+20 = 3w.

20 = 2w

10 = w.

So our original rectangle is 10ft x 20ft.

It's good to check the answer. Original area will be 10 x 20 = 200 sq.ft

Second rectangle will be 20ft x 30ft = 600 sq. ft, which is 3 times the original area as required.