The problem states that a rectangle has a length of $x$ cm and a width of $(x - 1)$ cm. The perimeter of the rectangle is 16 cm. We need to find the value of $x$.

1. Problem Description

The problem states that a rectangle has a length of $x$ cm and a width of $(x - 1)$ cm. The perimeter of the rectangle is 16 cm. We need to find the value of $x$.

2. Solution Steps

The formula for the perimeter of a rectangle is:

$P = 2l + 2w$

where $P$ is the perimeter, $l$ is the length, and $w$ is the width. We are given that $P = 16$, $l = x$, and $w = x - 1$. Substituting these values into the perimeter formula, we get:

$16 = 2(x) + 2(x - 1)$

Now we solve for $x$:

$16 = 2x + 2x - 2$

$16 = 4x - 2$

$16 + 2 = 4x$

$18 = 4x$

$x = \frac{18}{4}$

$x = \frac{9}{2}$

$x = 4\frac{1}{2}$

3. Final Answer

The value of $x$ is $4\frac{1}{2}$ cm.

The correct answer is C. $4\frac{1}{2}$ cm.