To solve the problem, we need to first find the breadth of the rectangular carpet and then use the formula for the perimeter of a rectangle.
### Step 1: Determine the Breadth
We are given that the breadth (B) of the carpet is [tex]\(\frac{1}{3}\)[/tex] of its length (L). If the length is denoted as [tex]\(x\)[/tex], then the breadth will be:
[tex]\[ B = \frac{1}{3} \times x = \frac{x}{3} \][/tex]
### Step 2: Calculate the Perimeter
The perimeter (P) of a rectangle is given by the formula:
[tex]\[ P = 2 \times (L + B) \][/tex]
Substituting the values for length [tex]\(L = x\)[/tex] and breadth [tex]\(B = \frac{x}{3}\)[/tex]:
[tex]\[ P = 2 \times \left(x + \frac{x}{3}\right) \][/tex]
### Step 3: Simplify the Expression
To simplify the expression inside the parentheses:
[tex]\[ x + \frac{x}{3} = \frac{3x}{3} + \frac{x}{3} = \frac{3x + x}{3} = \frac{4x}{3} \][/tex]
Thus, the perimeter becomes:
[tex]\[ P = 2 \times \frac{4x}{3} = \frac{8x}{3} \][/tex]
### Step 4: Determine the Correct Answer
From the available options, the correct perimeter is [tex]\(\frac{8}{3} x\)[/tex].
Therefore, the correct answer is:
C. [tex]\(\frac{8}{3} x\)[/tex]
