Question

Joshua is designing a rectangular mirror. He let w = the width, in inches, of the mirror. The length of the mirror will be 6 inches more than the width. The perimeter of the mirror will be less than 96 inches and greater than 76 inches. Which of the following inequalities shows the possible widths, in inches, of the mirror?

Answer 1

16 < w < 21

Explanation:

Given that :

Width if mirror = w

Length of mirror = l

L = 6 + w

Perimeter of mirror < 96 and > 76

Possible width of the mirror

Perimeter of a rectangle :

2(l + w)

2(6 + w + w)

= 2(6 + 2w)

= 12 + 4w

Hence,

76 < perimeter < 96

76 < 12 + 4w < 96

76 - 12 < 4w < 96 - 12

64 < 4w < 84

16 < w < 21