Final answer:
By using the Pythagorean theorem, we can find that the straight-line distance through the pond from point A to point B is approximately 53 meters. Subtracting this from the total distance walked (75 meters) gives us a savings of 22 meters, which unfortunately doesn't match any of the provided options.
Step-by-step explanation:
To calculate how many meters would be saved if it were possible to walk straight through the pond from point A to point B, we can use the Pythagorean theorem. The distances walked south and east form a right-angled triangle, with the legs being the paths walked to avoid the pond, and the hypotenuse being the straight path through the pond.
The two legs of the triangle are:
- Southward leg: 34 meters
- Eastward leg: 41 meters
To find the hypotenuse (the distance through the pond), we calculate:
Distance through the pond = √(34² + 41²)
= √(1156 + 1681)
= √(2837)
= 53.2 meters (to the nearest meter: 53 meters)
The savings in distance can be found by subtracting the straight-line distance (hypotenuse) from the sum of the two legs walked:
Meters saved = (34 + 41) - 53
= 75 - 53
= 22 meters
However, there seems to be a discrepancy with the provided options. According to the calculated distance saved, none of the options (A) 7 meters, (B) 75 meters, (C) 53 meters, (D) 2,837 meters exactly match the correct answer of 22 meters. If this is a case of a typo or error in the options, please double-check the question or options provided.