A rectangular swimming pool is twice as long as it is wide. A small 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.: *
call the width w
then the length is 2w
then the total width including the walkway on each side is (w+4)
and the length including the walkway on each end is
(2w+4)
We are told that the total area including the walkway minus the area of the pool itself is 196 ft^2
so
(2w+4)(w+4) - 2w^2 = 196
2 w^2 + 12 w + 16 - 2 w^2 = 196
You can take it from there I think
I get 15 by 30
Why is it w+4 instead of w+2
because there is 2 feet of concrete on each side of the pool. 2+2=4
nvm lol
To find the dimensions of the pool, we can set up a system of equations based on the given information.
Let's assume the width of the pool is "x" feet. Since the length is twice the width, the length of the pool is "2x" feet.
The area of the pool is equal to the length multiplied by the width: Area of the pool = length * width
So, for the pool, we have the equation:
Area of the pool = 2x * x = 2x^2
Now let's consider the walkway. We are given that the walkway is a constant 2 feet wide and has an area of 196 square feet.
The total area of the walkway is equal to the area of the larger rectangle minus the area of the pool.
So, we have:
Area of the walkway = (2x + 4) * (x + 4) - 2x^2
Given that the area of the walkway is 196 square feet, we can set up the equation:
(2x + 4) * (x + 4) - 2x^2 = 196
Now we can solve this equation to find the value of x, which represents the width of the pool.
Expanding the equation, we get:
(2x^2 + 12x + 16) - 2x^2 = 196
Combining like terms:
12x + 16 = 196
Simplifying:
12x = 180
Dividing both sides by 12, we find:
x = 15
Therefore, the width of the pool is 15 feet, and the length of the pool is twice the width, which is 30 feet.
So, the dimensions of the pool are 15 feet (width) and 30 feet (length).