Question

The perimeter of a square must be greater than 102 inches but less than 138 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 a decimal form for numerical values.

Answer 1

Answer:

s ∈ (25.5,34.5)

''s'' is in inches unit

s ∈ IR

Step-by-step explanation:

We know that the perimeter of a square is $P=4s$

Where P is the perimeter and s is the length of a side.

We want the perimeter to be greater than 102 inches but less than 138 inches.

We can write :

102 inches < P < 138 inches

If we replace P = 4s in the expression :

102 inches < 4s < 138 inches

Dividing by ''4''

25.5 inches < s < 34.5 inches

If we want the perimeter to be greater than 102 inches but less than 138 inches the length of a side must be greater than 25.5 inches but less than 34.5 inches.

Writing this in interval notation

s ∈ (25.5,34.5)

s ∈ IR