Question

To get from point A to point C you must avoid walking through a pond. You must walk 34 m south and 41 m east. How many meters would be saved if it were possible to make a way through the pond? Use the digram below to help. Write out the calculations on scrap paper and choose your final answer! (1 Point)

Answer 1

To solve the problem, we can visualize the situation as a right triangle formed by the south and east movements.

1. **Calculate the straight-line distance (hypotenuse) from Point A to Point C using the Pythagorean theorem:**
\[
\text{Distance} = \sqrt{(34 \text{ m})^2 + (41 \text{ m})^2}
\]

2. **Perform the calculations:**
\[
= \sqrt{1156 + 1681}
\]
\[
= \sqrt{2837}
\]
\[
\approx 53.24 \text{ m}
\]

3. **Now calculate the total distance walked around the pond:**
\[
\text{Total walked distance} = 34 \text{ m} + 41 \text{ m} = 75 \text{ m}
\]

4. **Determine the distance saved if walking directly through the pond:**
\[
\text{Distance saved} = \text{Total walked distance} - \text{Straight-line distance}
\]
\[
= 75 \text{ m} - 53.24 \text{ m} \approx 21.76 \text{ m}
\]

Thus, the distance saved by walking directly through the pond would be approximately **21.76 meters**.