Question

Renee is creating a rectangular garden in her backyard. The length of the garden is 8 feet. The perimeter of the garden must be at least 30 feet and no more than 32 feet. Use a compound inequality to find the range of values for the width w of the garden.

Answer 1

The appropriate compound inequality is then 14 ft ≤ W ≤ 16 ft

Explanation:

30 ft perimeter: P = 30 ft = 2L + 2W = 2(8 ft) + 2W

Solving for W, we get: 30 ft - 16 ft = 14 ft. The minimum width, W, is 14 ft.

32 ft perimeter:

P = 32 ft = 2L + 2W = 2(8 ft) + 2W

Solving for W, we get: 32 ft - 16 ft = 16 ft. The minimum width, W, is 16 ft.

The appropriate compound inequality is then 14 ft ≤ W ≤ 16 ft

Answer 2

Range of width = [7,8]

Explanation:

Let w be the width of garden,

The length of garden, l = 8 feet

We have perimeter = 2 x ( length + width)

Perimeter = 2 x ( 8 + w)

The perimeter of the garden must be at least 30 feet and no more than 32 feet.

That is

30 ≤ 2 x ( 8 + w) ≤ 32

15 ≤ 8 + w ≤ 16

7 ≤ w ≤ 8

So range of width = [7,8]