Question

A window in Lynn and​ Jorge's house needs to be replaced. The rectangular window is 3 feet 6 inches tall and 2 feet 7 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?
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Part 1
​(a) The perimeter of the window is
  
enter your response here inches. ​(Simplify your​ answer.)

Answer 1

To find the dimensions of the window in inches and then calculate the perimeter, we will follow these steps:

1. Convert the measurements of the window from feet and inches to inches alone.
2. Use the formula for the perimeter of a rectangle, which is \( P = 2 \times (length + width) \).
3. Calculate the total cost to insulate the perimeter.

### Step 1: Convert Measurements to Inches

**Height:**
- \(3\) feet \(6\) inches = \(3 \times 12 + 6 = 36 + 6 = 42\) inches

**Width:**
- \(2\) feet \(7\) inches = \(2 \times 12 + 7 = 24 + 7 = 31\) inches

### Step 2: Calculate the Perimeter

Now that we have the height and width in inches:
- Height = \(42\) inches
- Width = \(31\) inches

Using the perimeter formula:
\[
P = 2 \times (Height + Width) = 2 \times (42 + 31)
\]
Calculating the sum:
\[
42 + 31 = 73
\]

Now substitute back into the perimeter formula:
\[
P = 2 \times 73 = 146 \text{ inches}
\]

### Step 3: Calculate the Cost to Insulate the Perimeter

The cost of insulation is \(0.40\) per inch.
\[
\text{Total Cost} = \text{Perimeter} \times \text{Cost per inch} = 146 \times 0.40
\]
Calculating the cost:
\[
146 \times 0.40 = 58.4
\]

### Final Answers

(a) The perimeter of the window is **146 inches**.
(b) The cost to insulate the perimeter is **$58.40**.