Question

The perimeter of a square is to be at least 18 feet, but not more than 48 feet. Find all possible values for the length of its sides.

a) 4.5 ft ≤ x ≤ 44 ft
b) 9 ft
c) 4.5 ft ≤ x ≤ 12 ft
d) 9 ft ≤ x ≤ 24 ft

Answer 1

The possible values for the side length of a square with a perimeter of at least 18 feet but not more than 48 feet are found by dividing the perimeter by 4, resulting in a range of 4.5 ft ≤ x ≤ 12 ft.

Step-by-step explanation:

The question asks us to find the possible values for the length of the sides of a square given a perimeter range. We know that the perimeter of a square (P) is the total length around the square, which can be calculated with the formula P=4a, where a is the length of one side of the square. Therefore, for a perimeter of at least 18 feet but no more than 48 feet, we divide by 4 to get the corresponding side lengths.

For the minimum perimeter of 18 feet:

18 feet ÷ 4 = 4.5 feet (minimum side length)

For the maximum perimeter of 48 feet:

48 feet ÷ 4 = 12 feet (maximum side length)

So, the side length of the square (x) can be any value in the range 4.5 feet ≤ x ≤ 12 feet. Hence, the correct answer is c) 4.5 ft ≤ x ≤ 12 ft.