Final answer:
To find the area of the rectangular swimming pool, we used the Pythagorean theorem to calculate the missing width and then the area formula. The area is approximately 29.92 square meters.
Step-by-step explanation:
The student has asked how to determine the area of a rectangular swimming pool given its length and diagonal distance. To find the area, we need to find the width of the pool using the Pythagorean theorem. Since the pool is a rectangle, the diagonal forms a right triangle with the length and width.
Let's call the length of the pool 'l', the width 'w', and the diagonal 'd'. We are given that l = 8.5 m and d = 9.2 m. The Pythagorean theorem tells us that:
l2 + w2 = d2
Substituting the values we have:
8.52 + w2 = 9.22
Solving for 'w' gives:
w2 = 9.22 - 8.52
w2 = 84.64 - 72.25
w2 = 12.39
w = √12.39 ≈ 3.52 m (rounded to two decimal places)
Now that we have the width, we can calculate the area of the pool:
Area = length × width
Area = 8.5 m × 3.52 m ≈ 29.92 m2
So, the area of the pool is approximately 29.92 square meters.