A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
A large swimming pool has a perimeter of 1,102 meters, this rectangular-shaped pool is 40 meters longer than 6 times its width. Find its dimensions
To find the dimensions of the pool, let's denote the width of the pool as "W" and the length of the pool as "L".
We know that the pool is twice as long as it is wide, so we can say that L = 2W.
The total area of the pool and the walkway combined is equal to the area of the pool plus the area of the walkway.
Since the walkway is a constant 2 feet wide around the pool, the overall dimensions of the pool and the walkway would be (L + 4) by (W + 4).
Therefore, the equation becomes:
(L + 4) * (W + 4) = Area of pool + Area of walkway
Substituting the values, the equation becomes:
(L + 4) * (W + 4) = L * W + 196
Now, let's substitute L = 2W into the equation:
(2W + 4) * (W + 4) = 2W * W + 196
Expanding the equation, we get:
2W^2 + 8W + 4W + 16 = 2W^2 + 196
Simplifying further:
2W^2 + 12W + 16 = 2W^2 + 196
Subtracting 2W^2 from both sides:
12W + 16 = 196
Subtracting 16 from both sides:
12W = 180
Dividing by 12:
W = 15
So, the width of the pool is 15 feet.
Substituting the value of W back into the equation L = 2W:
L = 2 * 15 = 30
Therefore, the length of the pool is 30 feet.
Hence, the dimensions of the pool are 30 feet by 15 feet.
(w+4)(2w+4)-w(2w) = 196
Solve for w, and then you figure the length, 2w.