Question

The length, l, of a rectangle is 3 inches greater than its width, w. The perimeter of the rectangle is at least 30 inches. Which inequalityshows the range of possible lengths of the rectangle?

Answer 1

l >= 9 and w >= 6

Explanation:

The perimeter of the rectangle can be found by:

→ Perimeter = (2 x length) + (2 x width) (1)

Since the length is 3 inches greater than the width:

→ l = w + 3

Also, the perimeter is at least 30 inches

If you substitute the values in the equation 1:

→ (2 x l) + (2 x w) >= 30

→ (2 x (w + 3)) + (2 x w) >= 30

→ 2 x w + 6 + (2 x w) >= 30

→ 4 x w >= 24

→ w >= 6

Since l = w + 3, l >= 9