The length of a pool is 3 feet more than twice its width. If the perimeter of the pool is 72 feet, find the dimensions of the pool by writing and solving a system of equations.
Width = W Ft.
Length = (2W + 3)Ft
P = 2W + 2(2W+3) = 72
2W + 4W+6 = 72
6W = 72-6 = 66
W = 11 Ft.
Length = 2*11 + 3 = 25 Ft
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the width of the pool is "x" feet.
According to the problem, the length of the pool is 3 feet more than twice its width. Thus, the length can be expressed as "2x + 3" feet.
The perimeter of a rectangle is given by the formula: P = 2(L + W), where P is the perimeter, L is the length, and W is the width.
Given that the perimeter of the pool is 72 feet, we can set up the equation:
72 = 2(2x + 3 + x)
Simplifying this equation, we have:
72 = 2(3x + 3)
Next, we distribute the 2 to both terms inside the parentheses:
72 = 6x + 6
Now, subtract 6 from both sides of the equation to isolate the 6x term:
72 - 6 = 6x
Simplifying further, we get:
66 = 6x
Finally, divide both sides of the equation by 6 to solve for x:
x = 66/6
x = 11
Therefore, the width of the pool is 11 feet.
To find the length, we can substitute the value of x into the expression for the length:
Length = 2x + 3
Length = 2(11) + 3
Length = 22 + 3
Length = 25
Therefore, the dimensions of the pool are width = 11 feet and length = 25 feet.