Final answer:
The width of the pool is 70 meters and the length is 440 meters.
Step-by-step explanation:
Let's define the width of the pool as 'w'.
The length of the pool is 20 meters longer than 6 times its width, so the length can be expressed as 6w + 20.
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given that the perimeter of the pool is 1020 meters, so we can set up the equation: 1020 = 2(6w + 20) + 2w
Simplifying the equation, we get: 1020 = 12w + 40 + 2w
Combining like terms, we have: 1020 = 14w + 40
Subtracting 40 from both sides of the equation, we get: 980 = 14w
Dividing both sides of the equation by 14, we get: w = 70
So the width of the pool is 70 meters.
Now, we can substitute this value of w into the expression for the length of the pool to find the length: L = 6w + 20 = 6(70) + 20 = 420 + 20 = 440
Therefore, the dimensions of the pool are 70 meters by 440 meters.