To determine the diagonal distance between the corners of the pool, we need to use the Pythagorean theorem. This theorem states that for a right-angled triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides.
Given:
- The width of the pool is 20 yards.
- The length of the pool is 60 yards.
Steps:
1. Square the width and the length.
- [tex]\(20^2 = 400\)[/tex]
- [tex]\(60^2 = 3600\)[/tex]
2. Add the squares of the width and the length.
- [tex]\( 400 + 3600 = 4000\)[/tex]
3. Take the square root of the sum to find the diagonal.
- [tex]\(\sqrt{4000} \approx 63.245553203367585\)[/tex]
Thus, the approximate diagonal distance between the diagonally opposite corners of the pool is about 63.25 yards.
Given the options, the closest value to the actual diagonal length of 63.25 yards is not listed directly, but if one had to pick an approximate option:
- 53 yards
- 55 yards
- 57 yards
- 72 yards
None of the given options is a close match to 63.25 yards. Therefore, it would be best to double-check the provided options or the calculations to ensure accuracy. The correct diagonal length here is approximately 63.25 yards.
