We can use the Pythagorean theorem to find the distance saved if it were possible to walk through the pond in a straight line. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
c^2 = a^2 + b^2
In this case, a = 34 meters (south) and b = 41 meters (east). We can plug these values into the theorem to find the length of the hypotenuse, which represents the straight-line distance through the pond:
c^2 = (34)^2 + (41)^2
c^2 = 1156 + 1681
c^2 = 2837
c = sqrt(2837)
c ≈ 53.26 meters
Now, we can find the distance saved by subtracting the straight-line distance through the pond from the total distance walking around it:
Distance saved = (34 + 41) - 53.26
Distance saved = 75 - 53.26
Distance saved ≈ 21.74 meters
To the nearest meter, approximately 22 meters would be saved if it were possible to walk through the pond.