Final answer:
The length and width of the rectangle are 18y and 15y, respectively.
Step-by-step explanation:
Let's use the given information to set up an equation. We are told that the length of the rectangle is 3y longer than its width. Let's represent the width as 'w'. So, the length would be 'w + 3y'.
The perimeter of a rectangle is given by the formula: P = 2(length + width). So, we can write the equation as:
66y = 2[(w + 3y) + w]
Simplifying the equation, we get:
66y = 2(2w + 3y)
66y = 4w + 6y
Combine like terms:
66y - 6y = 4w
60y = 4w
Divide both sides by 4 to solve for 'w':
15y = w
So, the width of the rectangle is 15y. Now, substitute this value back into the equation for the length:
Length = 15y + 3y = 18y
Therefore, the length of the rectangle is 18y and the width is 15y.