Question
Each side of a square is 5 miles long. How much distance is saved by a bird that would fly directly from point A to point B instead of a car that took a direct route south and then east? Round your answer to the nearest tenth of a mile.
Answers
GPT-4o mini
To determine the distance saved by the bird flying directly from point A to point B instead of the car's route, we first need to compute both distances.
1. **Bird's Distance**: Since the bird flies directly from point A to point B, we can think of this as the diagonal of a square. The formula for the diagonal \(d\) of a square with side length \(s\) is given by:
\[
d = s \sqrt{2}
\]
Here, each side of the square \(s\) is 5 miles. Thus, the diagonal distance the bird flies is:
\[
d = 5 \sqrt{2} \approx 5 \times 1.414 = 7.07 \text{ miles}
\]
2. **Car's Distance**: The car takes a route that goes directly south and then east. This means the car travels down one side of the square (5 miles) and then across the next side of the square (5 miles). The total distance traveled by the car is:
\[
\text{Total distance} = 5 + 5 = 10 \text{ miles}
\]
3. **Distance Saved**: The distance saved by the bird compared to the car is the difference between the car's distance and the bird's distance:
\[
\text{Distance saved} = \text{Car's Distance} - \text{Bird's Distance} = 10 - 7.07 \approx 2.93 \text{ miles}
\]
4. **Rounding**: Rounding to the nearest tenth of a mile gives:
\[
\text{Distance saved} \approx 2.9 \text{ miles}
\]
Therefore, the distance saved by the bird that flies directly from point A to point B instead of following the car's route is approximately **2.9 miles**.
1. **Bird's Distance**: Since the bird flies directly from point A to point B, we can think of this as the diagonal of a square. The formula for the diagonal \(d\) of a square with side length \(s\) is given by:
\[
d = s \sqrt{2}
\]
Here, each side of the square \(s\) is 5 miles. Thus, the diagonal distance the bird flies is:
\[
d = 5 \sqrt{2} \approx 5 \times 1.414 = 7.07 \text{ miles}
\]
2. **Car's Distance**: The car takes a route that goes directly south and then east. This means the car travels down one side of the square (5 miles) and then across the next side of the square (5 miles). The total distance traveled by the car is:
\[
\text{Total distance} = 5 + 5 = 10 \text{ miles}
\]
3. **Distance Saved**: The distance saved by the bird compared to the car is the difference between the car's distance and the bird's distance:
\[
\text{Distance saved} = \text{Car's Distance} - \text{Bird's Distance} = 10 - 7.07 \approx 2.93 \text{ miles}
\]
4. **Rounding**: Rounding to the nearest tenth of a mile gives:
\[
\text{Distance saved} \approx 2.9 \text{ miles}
\]
Therefore, the distance saved by the bird that flies directly from point A to point B instead of following the car's route is approximately **2.9 miles**.