Final answer:
The perimeter of the rectangle in terms of the width x is calculated using the formula P = 2((1/5)x - 2) + 2x, which simplifies to P = (12/5)x - 4 units.
Step-by-step explanation:
To determine the perimeter of a rectangle given the relationship between the rectangle's length and width, first express the length in terms of the width. The problem states that the length (L) is 2 units shorter than one-fifth of the width (x). Thus, we can express the length as:
L = (1/5)x - 2
The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width. Now, given that the width is x, we can substitute the expression for L into the perimeter formula:
P = 2((1/5)x - 2) + 2x
This simplifies to:
P = (2/5)x - 4 + 2x
Combining like terms, we get:
P = (12/5)x - 4
Thus, the perimeter of the rectangle in terms of the width x is (12/5)x - 4 units.