Question

A rectangle has side lengths, in centimetres, of w and w-2.

The perimeter of the rectangle in smaller than 24cm. Use this information to write a double inequality for w.

Answer 1

1. P = 0 < 2w + 2(w-2) < 24

2. 1 < w < 7

Explanation:

1. The formula for perimeter is 2 times the Length plus 2 times the width of the side.

P = 2L + 2W

2. If the perimeter needs to be less than 24 cm, then we can create the following inequality because the perimeter has to be greater than zero as well.

0 < 2L + 2W < 24 cm

3. We can now plug the length and width values into the inequality.

L = w and W = w - 2

0 < 2w + 2(w-2) < 24

4. Now we can combine like terms and simplify.

0 < 2w + 2w - 4 < 24

0 < 4w - 4 < 24

4 < 4w < 28

1 < w < 7