Question

A rectangle's length is twice as long as it is wide. If the length is doubled and its breadth

is halved, the new rectangle will have a perimeter of 12 m longer than the original
rectangle's perimeter.
What are the dimensions of these rectangles?

Answer 1

Let's assume that the width of the original rectangle is "w". Therefore, the length of the original rectangle is "2w".

The perimeter of the original rectangle is given by:
P1 = 2(l + w) = 2(2w + w) = 6w

If the length is doubled and the width is halved, the new length becomes "4w" and the new width becomes "0.5w". Therefore, the new perimeter is given by:
P2 = 2(l + w) = 2(4w + 0.5w) = 9w

We know that the new perimeter is 12 meters longer than the original perimeter. Therefore:
P2 - P1 = 9w - 6w = 12
3w = 12
w = 4

Therefore, the width of the original rectangle is 4 meters and the length of the original rectangle is 2w = 8 meters.

The width of the new rectangle is 0.5w = 2 meters and the length of the new rectangle is 4w = 16 meters.