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 5 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 $0.60 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.
(a) Find the perimeter of the window in inches.
(b) If the perimeter needs to be sealed with insulation that is $0.60 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.
Answers
GPT-4o mini
To solve the problem, we'll start by converting the measurements of the window from feet and inches to just inches.
### Step 1: Convert Measurements to Inches
1. **Height**: The window is 3 feet 6 inches tall.
- Convert feet to inches: \(3 \text{ feet} = 3 \times 12 = 36 \text{ inches}\)
- Add the remaining inches: \(36 \text{ inches} + 6 \text{ inches} = 42 \text{ inches}\)
2. **Width**: The window is 2 feet 5 inches wide.
- Convert feet to inches: \(2 \text{ feet} = 2 \times 12 = 24 \text{ inches}\)
- Add the remaining inches: \(24 \text{ inches} + 5 \text{ inches} = 29 \text{ inches}\)
Now we have:
- Height = 42 inches
- Width = 29 inches
### Part 1: Calculate the Perimeter
The perimeter \(P\) of a rectangle can be calculated using the formula:
\[
P = 2 \times (\text{Height} + \text{Width})
\]
Substituting the values:
\[
P = 2 \times (42 + 29) = 2 \times 71 = 142 \text{ inches}
\]
So, the perimeter of the window is **142 inches**.
### Part 2: Calculate the Cost to Insulate
The cost to insulate the perimeter is given at a rate of $0.60 per inch. Therefore, the total cost \(C\) can be calculated using:
\[
C = \text{Perimeter} \times \text{Cost per inch} = 142 \times 0.60
\]
Calculating the total cost:
\[
C = 142 \times 0.60 = 85.20
\]
Thus, it will cost **$85.20** to insulate the perimeter.
### Final Answers
Part 1: The perimeter of the window is **142 inches**.
Part 2: It will cost **$85.20** to insulate the perimeter.
### Step 1: Convert Measurements to Inches
1. **Height**: The window is 3 feet 6 inches tall.
- Convert feet to inches: \(3 \text{ feet} = 3 \times 12 = 36 \text{ inches}\)
- Add the remaining inches: \(36 \text{ inches} + 6 \text{ inches} = 42 \text{ inches}\)
2. **Width**: The window is 2 feet 5 inches wide.
- Convert feet to inches: \(2 \text{ feet} = 2 \times 12 = 24 \text{ inches}\)
- Add the remaining inches: \(24 \text{ inches} + 5 \text{ inches} = 29 \text{ inches}\)
Now we have:
- Height = 42 inches
- Width = 29 inches
### Part 1: Calculate the Perimeter
The perimeter \(P\) of a rectangle can be calculated using the formula:
\[
P = 2 \times (\text{Height} + \text{Width})
\]
Substituting the values:
\[
P = 2 \times (42 + 29) = 2 \times 71 = 142 \text{ inches}
\]
So, the perimeter of the window is **142 inches**.
### Part 2: Calculate the Cost to Insulate
The cost to insulate the perimeter is given at a rate of $0.60 per inch. Therefore, the total cost \(C\) can be calculated using:
\[
C = \text{Perimeter} \times \text{Cost per inch} = 142 \times 0.60
\]
Calculating the total cost:
\[
C = 142 \times 0.60 = 85.20
\]
Thus, it will cost **$85.20** to insulate the perimeter.
### Final Answers
Part 1: The perimeter of the window is **142 inches**.
Part 2: It will cost **$85.20** to insulate the perimeter.