To solve the problem, we need to find the missing side $x$ of the trapezoid using the given perimeter and side lengths.

Step-by-step solution:

1. The formula for the perimeter of a trapezoid is the sum of all its side lengths: $P = a + b + c + d$ where $a = 23 \, \text{in}, b = 5 \, \text{in}, c = 9 \, \text{in}, \text{and } d = x$.

2. The perimeter $P$ is given as $67 \, \text{in}$. Substituting the known values: $67 = 23 + 5 + 9 + x$

3. Simplify: $67 = 37 + x$

4. Solve for $x$: $x = 67 - 37 = 30 \, \text{in}.$

Final Answer:

The missing side length $x$ is 30 inches.

Let me know if you'd like more details or explanations!

Related Questions:

1. How do you calculate the perimeter of other polygons like triangles or rectangles?
2. What are some properties of trapezoids?
3. How do you solve for a missing side when the area of a trapezoid is given instead of the perimeter?
4. What types of problems involve trapezoids in real-world applications?
5. Can you explore how to check if a given set of sides forms a trapezoid?

Tip: Always double-check your addition and subtraction when solving for missing sides in geometry problems involving perimeter.