Question
Javier is building a patio next to his house. He plans to add a brick border that extends all the way around the perimeter of the patio. The patio will be 8ft. by 10ft., and the border will be 2ft. wide. How many square feet of brick will he need?(1 point)
Responses
88 ft.2
88 ft. squared
80 ft.2
80 ft. squared
168 ft.2
168 ft. squared
16 ft.2
Responses
88 ft.2
88 ft. squared
80 ft.2
80 ft. squared
168 ft.2
168 ft. squared
16 ft.2
Answers
GPT-4o mini
To calculate the area of the brick border that will extend around Javier's patio, we first need to find the dimensions of the entire area that includes both the patio and the border.
1. **Calculate the dimensions of the entire area**:
- The patio measures 8 ft by 10 ft.
- Because the border is 2 ft wide, we need to account for the border on all sides of the patio.
- The total width of the area including the border along the length will be \(10 + 2 + 2 = 14\) ft (adding 2 ft for each side).
- The total width along the width will be \(8 + 2 + 2 = 12\) ft (adding 2 ft for each side).
2. **Calculate the area of the entire area with the border**:
- Area of the entire rectangle (patio + border) = length × width = \(14 \text{ ft} \times 12 \text{ ft} = 168 \text{ ft}^2\).
3. **Calculate the area of the patio**:
- Area of the patio = length × width = \(10 \text{ ft} \times 8 \text{ ft} = 80 \text{ ft}^2\).
4. **Calculate the area of the brick border**:
- Area of the brick border = Area of the entire area - Area of the patio = \(168 \text{ ft}^2 - 80 \text{ ft}^2 = 88 \text{ ft}^2\).
Thus, Javier will need **88 ft²** of brick for the border.
So the correct response is:
**88 ft.²** (or **88 ft squared**).
1. **Calculate the dimensions of the entire area**:
- The patio measures 8 ft by 10 ft.
- Because the border is 2 ft wide, we need to account for the border on all sides of the patio.
- The total width of the area including the border along the length will be \(10 + 2 + 2 = 14\) ft (adding 2 ft for each side).
- The total width along the width will be \(8 + 2 + 2 = 12\) ft (adding 2 ft for each side).
2. **Calculate the area of the entire area with the border**:
- Area of the entire rectangle (patio + border) = length × width = \(14 \text{ ft} \times 12 \text{ ft} = 168 \text{ ft}^2\).
3. **Calculate the area of the patio**:
- Area of the patio = length × width = \(10 \text{ ft} \times 8 \text{ ft} = 80 \text{ ft}^2\).
4. **Calculate the area of the brick border**:
- Area of the brick border = Area of the entire area - Area of the patio = \(168 \text{ ft}^2 - 80 \text{ ft}^2 = 88 \text{ ft}^2\).
Thus, Javier will need **88 ft²** of brick for the border.
So the correct response is:
**88 ft.²** (or **88 ft squared**).