perimeter of a square

Question

The perimeter of a square must be greater than 128 inches but less than 154 inches. Find the range of possible side lengths that satisfy these conditions. (Hint: The perimeter of a square is given by P=4s, where s represents the length of a side).

Express your answer in interval notation. Use decimal form for numerical values.

Answer 1

The range of possible side lengths can be found by calculating the side length of a square with a perimeter of 128 inches and a square with a perimeter of 154 inches. You essentially just solve for the side length of two squares.

128=4s

*Divide by 4*

s=32

154=4s

*Divide by 4*

s=38.5

Given that the range is greater than and less than we use () instead of []. Therefore, in interval notation our answer would be (32 , 38.5), i.e. the range of possible side lengths is greater than 32 and less than 38.5.

Answer 2

128 < p < 154

128 < 4s < 154

32 < s < 38.4