To find the length of the diagonal of the rectangular swimming pool, we'll use the Pythagorean Theorem. The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides.
Given:
- Width (one side of the rectangle) = 19 meters
- Length (the other side of the rectangle) = 35 meters
Let's denote the length of the diagonal as [tex]\( d \)[/tex].
According to the Pythagorean Theorem:
[tex]\[ d^2 = \text{width}^2 + \text{length}^2 \][/tex]
Substitute the given values:
[tex]\[ d^2 = 19^2 + 35^2 \][/tex]
Calculate the squares:
[tex]\[ 19^2 = 361 \][/tex]
[tex]\[ 35^2 = 1225 \][/tex]
Add the results:
[tex]\[ d^2 = 361 + 1225 \][/tex]
[tex]\[ d^2 = 1586 \][/tex]
To find [tex]\( d \)[/tex], take the square root of 1586:
[tex]\[ d = \sqrt{1586} \][/tex]
Calculate the square root:
[tex]\[ d \approx 39.827 \][/tex]
Round this value to the nearest tenth:
[tex]\[ d \approx 39.8 \][/tex]
Therefore, the length of the diagonal of the pool, rounded to the nearest tenth, is 39.8 meters.
So, the correct answer is:
(A) 39.8 m
