The perimeter of a rectangle is given by P = 2W + 2L where W is the width and L is the length. The length of a rectangle is 3 more than twice its width. The perimeter of the rectangle is 66 meters. What is the length and width of the rectangle?
2 W + 2 (2 W + 3) = 66
6 W + 6 = 66
6 W = 60 etc
To solve this problem, we will use the information given about the perimeter equation and the relationship between the length and the width.
Let's start by assigning variables to the given information:
- Width: W
- Length: L
According to the problem, the length of the rectangle is 3 more than twice its width. We can express this relationship with the equation:
L = 2W + 3
The perimeter of a rectangle can be calculated using the formula:
P = 2W + 2L
The problem also states that the perimeter of the rectangle is 66 meters, so we can write:
66 = 2W + 2L
Now we can substitute the expression for L from the first equation into the second equation:
66 = 2W + 2(2W + 3)
Simplifying this equation gives:
66 = 2W + 4W + 6
Combine the like terms:
66 = 6W + 6
Subtract 6 from both sides:
60 = 6W
Divide both sides by 6 to solve for W:
W = 10
Now that we have found the value of W, we can substitute it back into the equation for L:
L = 2W + 3
L = 2(10) + 3
L = 20 + 3
L = 23
Therefore, the length of the rectangle is 23 meters and the width is 10 meters.