Rectangle Perimeter Problem: Solve for X When Perimeter = 23 and Height = 5

To solve this problem, we'll follow these steps:

• Step 1: Use the formula for the perimeter of a rectangle.
• Step 2: Substitute the given values into the equation.
• Step 3: Solve the resulting equation for $X$.
• Step 4: Confirm the resulting value with the choices provided.

Step 1: The perimeter $P$ of a rectangle is given by the formula:
$P = 2(l + w)$, where $l$ is the length and $w$ is the width.

Step 2: Substitute the known values into the formula:
$23 = 2(5 + X)$

Step 3: Solve for $X$:

• Divide both sides by 2:
  $23 = 2(5 + X) \Rightarrow \frac{23}{2} = 5 + X$
• Simplify $\frac{23}{2}$ to get $11.5$:
  $11.5 = 5 + X$
• Subtract 5 from both sides to isolate $X$:
  $X = 11.5 - 5$
• Simplify to find $X = 6.5$

Therefore, the length of the missing side $X$ is $6.5$.