Question

Cheryl is creating a rectangular garden in her backyard. The length of the garden is 11 feet. The perimeter of the garden must be at least 36 feet and no more than 38 feet. Use a compound inequality to find the range of values for the width w of the garden.

Answer 1

The range of values for the width is within 7 to 8 feet i.e 7 feet, 7.5 feet, 8 feet.

Explanation:

The formula for the perimeter of a rectangle is 2( L + W)

Perimeter = P ≥ 36 and P ≤ 38

hence, the perimeter is within the range of 36 and 38 feet ( i.e 36, 37, 38).

L = 11 feet

When Perimeter is 36 feet

36 = 2L + 2 W

36 = 2(11)+ 2 W

36 = 22 + 2W

36 - 22 = 2W

14 = 2W

W = 14/2

W = 7 feet

When Perimeter is 37 feet

37 = 2L + 2 W

37 = 2(11)+ 2 W

37 = 22 + 2W

37 - 22 = 2W

15 = 2W

W = 14/2

W = 7.5 feet

When Perimeter is 38 feet

38 = 2L + 2 W

38 = 2(11)+ 2 W

38 = 22 + 2W

38 - 22 = 2W

16 = 2W

W = 16/2

W = 8 feet

The range of values for the width is within 7 to 8 feet i.e 7 feet, 7.5 feet, 8 feet.