Question
Special Right Triangles Quick Check 5 of 55 of 5 Items Question Jamila keeps alpacas on a 1-acre, square lot near her home. She has 6 alpacas and wants to build a fence diagonally to split the herd in two. If an acre is 209 feet long, how many feet, to the nearest foot, of fencing does Jamila need? (1 point) Responses 362 feet 362 feet 296 feet 296 feet 148 feet 148 feet 247 feet 247 feet Skip to navigation page 15 of 15
Answers
GPT-4o mini
To determine how much fencing Jamila needs to build a diagonal fence to split her square lot, we first need to calculate the length of the diagonal of a square.
1. **Find the area of the square lot in square feet**: Since 1 acre = 43,560 square feet, and the area of a square is given by the formula \( \text{Area} = \text{side length}^2 \), we can find the side length by taking the square root of the area:
\[
\text{side length} = \sqrt{43,560} \approx 208.7 \text{ feet}
\]
2. **Calculate the diagonal**: The diagonal \( d \) of a square can be found using the formula \( d = \text{side length} \times \sqrt{2} \):
\[
d = 208.7 \times \sqrt{2} \approx 208.7 \times 1.414 \approx 295.5 \text{ feet}
\]
3. **Rounding**: Rounding 295.5 feet to the nearest foot gives us 296 feet.
Thus, Jamila needs approximately **296 feet** of fencing to build the diagonal fence.
1. **Find the area of the square lot in square feet**: Since 1 acre = 43,560 square feet, and the area of a square is given by the formula \( \text{Area} = \text{side length}^2 \), we can find the side length by taking the square root of the area:
\[
\text{side length} = \sqrt{43,560} \approx 208.7 \text{ feet}
\]
2. **Calculate the diagonal**: The diagonal \( d \) of a square can be found using the formula \( d = \text{side length} \times \sqrt{2} \):
\[
d = 208.7 \times \sqrt{2} \approx 208.7 \times 1.414 \approx 295.5 \text{ feet}
\]
3. **Rounding**: Rounding 295.5 feet to the nearest foot gives us 296 feet.
Thus, Jamila needs approximately **296 feet** of fencing to build the diagonal fence.