Final answer:
By applying the Pythagorean Theorem, it is calculated that walking directly through the pond saves approximately 22 meters, compared to walking 34 meters south and 41 meters east around the pond. Since none of the answer options exactly match the calculated value, option A (20 meters) is the closest, although it is not exact.
Step-by-step explanation:
To determine how many meters would be saved if it were possible to walk through the pond, we can use the Pythagorean Theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this scenario, walking 34 meters south and then 41 meters east forms a right-angled triangle, where these two distances are the legs, and the direct path across the pond would be the hypotenuse.
According to the Pythagorean Theorem: c^2 = a^2 + b^2
Where c is the hypotenuse and a and b are the lengths of the other two sides. Substituting the given lengths:
- c^2 = 34^2 + 41^2
- c^2 = 1156 + 1681
- c^2 = 2837
- c = √2837
- c ≈ 53.3 meters (to the nearest meter)
The distance walked avoiding the pond is 34 + 41 = 75 meters. The distance walked directly through the pond (hypotenuse) is approximately 53 meters. Therefore, the distance saved if walking through the pond is 75 - 53 = 22 meters. However, since the options given in the question are 20, 50, 60, and 74 meters, none of these are correct. The closest to the calculated value of 22 would be option A, 20 meters, but this is not an accurate reflection of the calculated savings.