Question

Leah is making a square wooden picture frame for woodworking class. After dividing a piece of wood she wants to use into 4 equal pieces, Leah figures each side of her frame can be at most 12 inches long.
Let x represent the perimeter of the picture frame. Which inequality describes the problem?
Solve the inequality. Then, complete the sentence to describe the solution.
The perimeter of the picture frame will be at most inches.

Answer 1

To start with, we need to understand the relationship between the side length of the square picture frame and its perimeter.

A square's perimeter \( P \) can be calculated using the formula:

\[
P = 4s
\]

where \( s \) is the length of one side of the square. Since Leah determined that each side of her frame can be at most 12 inches, we can set up the following inequality to represent the maximum side length:

\[
s \leq 12
\]

Now, we need to write the inequality for the perimeter based on this:

\[
P = 4s \leq 4 \times 12
\]

Calculating the right side:

\[
4 \times 12 = 48
\]

Thus, the inequality describing the problem becomes:

\[
P \leq 48
\]

Now, we solve it and find the maximum perimeter value:

The perimeter of the picture frame will be at most **48 inches**.