The perimeter of a rectangular pool is 84 feet. The width of the pool is half the length. What are the measurements of the rectangular pool?
L = 2W
P = 2L + 2W
84 = 2(2W) * 2W
84 = 6W
14 = W
Let's assume the length of the rectangular pool is x feet.
Given that the width of the pool is half the length, the width would be x/2 feet.
The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the perimeter is given as 84 feet.
So, we can write the equation as 84 = 2(x + x/2).
To solve this equation, we can simplify it by combining like terms:
84 = 2(3x/2)
Divide both sides by 2:
42 = 3x/2
To isolate x, multiply both sides by 2/3:
(2/3) * 42 = x
28 = x
Therefore, the length of the pool is 28 feet and the width is half of that, which is 28/2 = 14 feet.
To solve this problem, let's assume the length of the pool is "L" and the width is "W".
Given that the perimeter of the pool is 84 feet, we can set up an equation to represent this:
Perimeter = 2(length + width)
Since the width of the pool is half the length, we can replace "W" with "L/2" in the equation:
84 = 2(L + L/2)
Simplifying the equation, we get:
84 = 2(3/2L)
Now, let's solve for L. Divide both sides by 2:
42 = 3/2L
Multiply both sides by 2/3 to isolate L:
L = (42 * 2) / 3
L = 28
Therefore, the length of the rectangular pool is 28 feet. Now, we can find the width by replacing L in the equation:
W = L/2
W = 28/2
W = 14
Therefore, the width of the rectangular pool is 14 feet.
In summary, the measurements of the rectangular pool are 28 feet for the length and 14 feet for the width.