Question

The perimeter of a square must be greater than 62 inches but less than 86 inches. Find the range of possible side lengths that satisfy these conditions?

A) 15 < side length < 21

B) 14 < side length < 22

C) 13 < side length < 23

D) 12 < side length < 24

Answer 1

The range of possible side lengths for a square with a perimeter greater than 62 inches but less than 86 inches is more than 15.5 inches and less than 21.5 inches, which matches closest to option A: 15 < side length < 21.

Step-by-step explanation:

The perimeter of a square can be calculated using the formula P = 4s, where P represents the perimeter and s represents the side length of the square. To satisfy the conditions given (greater than 62 inches but less than 86 inches), we can set up the following inequalities:

62 < 4s < 86

Dividing all parts by 4 to solve for s, we get:

15.5 < s < 21.5

The possible range of the side lengths of the square must be greater than 15.5 inches and less than 21.5 inches. Thus, the closest range listed in the provided options that fits this solution is:

15 < side length < 21 (Option A)