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.

Answer 1

Let's visualize the situation. We have a square with each side measuring 5 miles. The car travels south and then east, while the bird takes a direct diagonal route from point A to point B.

1. **Car's Distance**:
- The car goes south 5 miles and then east 5 miles. The total distance traveled by the car is:
\[
\text{Car's Distance} = 5 \text{ miles} + 5 \text{ miles} = 10 \text{ miles}
\]

2. **Bird's Distance**:
- The bird flies diagonally from point A to point B. The diagonal distance can be calculated using the Pythagorean theorem because point A and point B form a right triangle with the two sides of the square (5 miles each) as the legs.
- Let \( d \) be the diagonal distance:
\[
d = \sqrt{(5 \text{ miles})^2 + (5 \text{ miles})^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2}
\]
- Approximating \( \sqrt{2} \) as approximately 1.414, we find:
\[
d \approx 5 \times 1.414 = 7.07 \text{ miles}
\]

3. **Distance Saved**:
- The distance saved by the bird compared to the car is:
\[
\text{Distance Saved} = \text{Car's Distance} - \text{Bird's Distance} = 10 \text{ miles} - 7.07 \text{ miles} = 2.93 \text{ miles}
\]

Rounding 2.93 miles to the nearest tenth of a mile gives:

\[
\text{Distance Saved} \approx 2.9 \text{ miles}
\]

Thus, the distance saved by the bird is approximately **2.9 miles**.