Question
Forrest wants to install trim around 1 door and 1 window.
The door frame is 3 feet across the top and 7 feet tall. The window is 3 x 4 feet.
The trim he selects costs $4.25 per linear foot. What is the total price of the trim?
Enter the total cost as your answer.
The door frame is 3 feet across the top and 7 feet tall. The window is 3 x 4 feet.
The trim he selects costs $4.25 per linear foot. What is the total price of the trim?
Enter the total cost as your answer.
Answers
GPT-4o mini
To calculate the total cost of the trim for the door and the window, we first need to find the perimeter of both and then multiply that by the cost per linear foot.
### Door:
- The dimensions of the door frame are 3 feet wide and 7 feet tall.
- The perimeter of the door frame can be calculated as follows:
\[
P_{\text{door}} = 2 \times ( \text{width} + \text{height}) = 2 \times (3 \text{ ft} + 7 \text{ ft}) = 2 \times 10 \text{ ft} = 20 \text{ ft}
\]
### Window:
- The dimensions of the window are 3 feet wide and 4 feet tall.
- The perimeter of the window frame can be calculated similarly:
\[
P_{\text{window}} = 2 \times ( \text{width} + \text{height}) = 2 \times (3 \text{ ft} + 4 \text{ ft}) = 2 \times 7 \text{ ft} = 14 \text{ ft}
\]
### Total Perimeter:
- Now, we add the perimeters of the door and the window:
\[
P_{\text{total}} = P_{\text{door}} + P_{\text{window}} = 20 \text{ ft} + 14 \text{ ft} = 34 \text{ ft}
\]
### Cost Calculation:
- The cost of the trim is given as $4.25 per linear foot. Therefore, the total cost for the trim is:
\[
\text{Total Cost} = P_{\text{total}} \times \text{cost per foot} = 34 \text{ ft} \times 4.25 \text{ dollars/ft} = 144.5 \text{ dollars}
\]
Thus, the total cost for the trim is **$144.50**.
### Door:
- The dimensions of the door frame are 3 feet wide and 7 feet tall.
- The perimeter of the door frame can be calculated as follows:
\[
P_{\text{door}} = 2 \times ( \text{width} + \text{height}) = 2 \times (3 \text{ ft} + 7 \text{ ft}) = 2 \times 10 \text{ ft} = 20 \text{ ft}
\]
### Window:
- The dimensions of the window are 3 feet wide and 4 feet tall.
- The perimeter of the window frame can be calculated similarly:
\[
P_{\text{window}} = 2 \times ( \text{width} + \text{height}) = 2 \times (3 \text{ ft} + 4 \text{ ft}) = 2 \times 7 \text{ ft} = 14 \text{ ft}
\]
### Total Perimeter:
- Now, we add the perimeters of the door and the window:
\[
P_{\text{total}} = P_{\text{door}} + P_{\text{window}} = 20 \text{ ft} + 14 \text{ ft} = 34 \text{ ft}
\]
### Cost Calculation:
- The cost of the trim is given as $4.25 per linear foot. Therefore, the total cost for the trim is:
\[
\text{Total Cost} = P_{\text{total}} \times \text{cost per foot} = 34 \text{ ft} \times 4.25 \text{ dollars/ft} = 144.5 \text{ dollars}
\]
Thus, the total cost for the trim is **$144.50**.