Let's break this problem into the steps provided in the image:

Step-by-step Solution

Step 1: Label the length and width of the rectangle.

• The length is given as $36 \, \text{ft}$.
• The width is labeled as $w$, as shown in the diagram.

Step 2: Write an expression for the sum of the length and width.

The sum of the length and width can be written as: $36 + w$

Step 3: Write an expression for twice the sum of the length and width.

To find twice the sum, multiply the expression from Step 2 by 2: $2 \times (36 + w) = 2(36 + w)$

Step 4: Write an equation for the perimeter of the exhibit.

The perimeter of a rectangle is defined as twice the sum of its length and width. We are given that the perimeter is $114 \, \text{ft}$. Thus, we write: $2(36 + w) = 114$

Now, let’s solve for $w$: $2(36 + w) = 114$ Divide both sides by 2: $36 + w = 57$ Subtract 36 from both sides: $w = 21$

Final Answer:

The width of the exhibit is $w = 21 \, \text{ft}$.

Would you like a detailed explanation of any step?

Related Questions:

1. What is the formula for the perimeter of a rectangle?
2. How can you check your solution for $w$?
3. What if the perimeter was instead 120 ft? How would the width change?
4. Can you generalize this solution for any perimeter and length?
5. How does doubling the width affect the perimeter?

Tip:

Always check your final answer by substituting it back into the original equation!