Question

A window in Lynn and​ Jorge's house needs to be replaced. The rectangular window is 3 feet 4 inches tall and 2 feet 9 inches wide. Change each of the measurements to inches.
​(a) Find the perimeter of the window in inches.
​(b) If the perimeter needs to be sealed with insulation that is ​$0.40 per​ inch, how much will it cost to insulate the​ perimeter?
Question content area bottom
Part 1
​(a) The perimeter of the window is
  
enter your response here inches. ​(Simplify your​ answer.)
Part 2
​(b) It will cost ​$
  
enter your response here to insulate the perimeter.

Answer 1

To solve the problem, let's first convert the measurements of the window to inches.

1. **Height conversion**:
- The window is 3 feet 4 inches tall.
- There are 12 inches in a foot, so:
- 3 feet = 3 × 12 = 36 inches
- Total height in inches = 36 inches + 4 inches = 40 inches.

2. **Width conversion**:
- The window is 2 feet 9 inches wide.
- 2 feet = 2 × 12 = 24 inches
- Total width in inches = 24 inches + 9 inches = 33 inches.

Now we have:
- Height = 40 inches
- Width = 33 inches

### Part 1: Calculate the perimeter

The formula for the perimeter \( P \) of a rectangle is:
\[
P = 2 \times (\text{height} + \text{width})
\]

Substituting the given values:
\[
P = 2 \times (40 + 33) = 2 \times 73 = 146 \text{ inches}
\]

So, the perimeter of the window is **146 inches**.

### Part 2: Calculate the cost to insulate the perimeter

The insulation cost is $0.40 per inch. To find the total cost \( C \):
\[
C = \text{perimeter} \times \text{cost per inch}
\]
\[
C = 146 \times 0.40 = 58.40
\]

Thus, the cost to insulate the perimeter will be **$58.40**.

### Summary of Answers
- **(a)** The perimeter of the window is **146 inches**.
- **(b)** It will cost **$58.40** to insulate the perimeter.