The perimeter of a square must be greater than 102
 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.



The perimeter \( P \) of a square is given by the formula:

\[
P = 4s
\]

where \( s \) represents the length of a side of the square. According to the problem, the perimeter must be greater than 102 inches but less than 154 inches. This can be written as the inequality:

\[
102 < 4s < 154
\]

### Step 1: Divide the entire inequality by 4 to isolate \( s \).

\[
\frac{102}{4} < s < \frac{154}{4}
\]

### Step 2: Perform the division.

\[
25.5 < s < 38.5
\]

### Final Answer:
The range of possible side lengths that satisfy the conditions is:

\[
(25.5, 38.5)
\]

This is the solution expressed in interval notation.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What is the perimeter of a square with a side length of 30 inches?
2. How would the interval change if the perimeter had to be between 200 and 300 inches?
3. What is the area of the square if the side length is 25.5 inches?
4. How do you find the side length if given the area of the square?
5. What happens to the perimeter if the side length is doubled?

**Tip:** For any square, dividing the perimeter by 4 always gives the length of a side!

The perimeter of a square must be greater than 102 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.

Learn how to find the range of possible side lengths for a square whose perimeter is greater than 102 inches but less than 154 inches. This problem uses the formula P = 4s to explore inequalities and geometry concepts, suitable for students in Grades 6-8.

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