Question

A window in Lynn and​ Jorge's house needs to be replaced. The rectangular window is 3 feet 7 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?

Answer 1

To solve this problem, we need to first convert the height and width of the window from feet and inches to just inches, then use that information to calculate the perimeter, and finally find the cost to insulate the perimeter.

### Step 1: Convert Measurements to Inches

1. **Height**:
- The window is 3 feet 7 inches tall.
- There are 12 inches in a foot, so:
\[
\text{Height in inches} = 3 \, \text{feet} \times 12 \, \text{inches/foot} + 7 \, \text{inches} = 36 \, \text{inches} + 7 \, \text{inches} = 43 \, \text{inches}
\]

2. **Width**:
- The window is 2 feet 9 inches wide.
- Again, converting to inches:
\[
\text{Width in inches} = 2 \, \text{feet} \times 12 \, \text{inches/foot} + 9 \, \text{inches} = 24 \, \text{inches} + 9 \, \text{inches} = 33 \, \text{inches}
\]

### Step 2: Calculate the Perimeter

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

Substituting the height and width we found:
\[
P = 2 \times (43 \, \text{inches} + 33 \, \text{inches}) = 2 \times 76 \, \text{inches} = 152 \, \text{inches}
\]

### Step 3: Calculate the Cost to Insulate

The cost to insulate the perimeter is given as \$0.40 per inch. To find the total cost, we multiply the perimeter by the cost per inch:
\[
\text{Cost} = \text{Perimeter} \times \text{Cost per inch} = 152 \, \text{inches} \times 0.40 \, \text{dollars/inch} = 60.8 \, \text{dollars}
\]

### Final Answers
(a) The perimeter of the window is **152 inches**.
(b) The cost to insulate the perimeter is **$60.80**.