Question

12 model with math a manager needs to rope off a rectangular section for a private party. the length of the section must be 7.6 meters. the manager can use no more than 28 meters of rope. what inequality could you use to find the possible width, w, of the roped - off section?

Explanation:

Step1: Recall the perimeter formula of a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width.

Step2: Substitute the known values and the inequality condition

We know that the length \( l = 7.6 \) meters and the perimeter \( P \leq 28 \) meters (since the manager can use no more than 28 meters of rope). Substituting \( l = 7.6 \) into the perimeter formula, we get:
\[
2(7.6 + w) \leq 28
\]

Step3: Simplify the inequality (optional, but to solve for \( w \))

First, divide both sides of the inequality by 2:
\[
7.6 + w \leq 14
\]
Then, subtract 7.6 from both sides:
\[
w \leq 14 - 7.6
\]
\[
w \leq 6.4
\]
But the question is just to find the inequality to use, so the main inequality from Step 2 is the one we need.

Answer:

The inequality is \( 2(7.6 + w) \leq 28 \) (and if solving for \( w \), we get \( w \leq 6.4 \), but the inequality to set up is \( 2(7.6 + w) \leq 28 \))