## Answer :

1.

**Identify the dimensions of the rectangle:**

- Given that the width of the rectangle is [tex]\( x \)[/tex].

- The area of the rectangle is represented by the expression [tex]\( A(x) = x(14 - x) \)[/tex].

- From the area expression, we can see that the length of the rectangle must be [tex]\( 14 - x \)[/tex].

2.

**Determine the expression for the perimeter:**

- The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:

[tex]\[ P = 2 (\text{width} + \text{length}) \][/tex]

- Here, the width is [tex]\( x \)[/tex] and the length is [tex]\( 14 - x \)[/tex].

- Substituting these values into the formula, we get:

[tex]\[ P = 2 (x + 14 - x) \][/tex]

3.

**Simplify the expression:**

- Inside the parentheses, [tex]\( x \)[/tex] and [tex]\( -x \)[/tex] cancel each other out:

[tex]\[ P = 2 (14) \][/tex]

- Simplifying further:

[tex]\[ P = 28 \][/tex]

So the perimeter of the rectangle is [tex]\( 28 \)[/tex].

**The correct answer is: A 28**