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We are given a shape with some known dimensions and a perimeter of 30 cm. The goal is to find the unknown length, labeled as a red box in the image. Let's break this down step by step:

1. **Known lengths**: 
   - The vertical sides are labeled as 3 cm, 4 cm, and 7 cm.
   - The horizontal side at the bottom is not directly labeled but can be inferred.
   - The red box at the top is the unknown length, which we will call \( x \) cm.
   
2. **Inferred lengths**:
   - The horizontal side at the bottom should be equal to the total width at the top minus the width of the vertical side at the top left (3 cm).
   - Since we do not know the total width at the top, we will represent it as the sum of \( x \) and the 3 cm on the left side.

3. **Perimeter calculation**:
   The perimeter of the shape is the sum of all its sides. Starting from the top left and moving clockwise, we have:
   \[
   \text{Perimeter} = x + 3 + 7 + 4 + \left(x + 3 \right) + 7 = 30 \text{ cm}
   \]

4. **Simplifying the equation**:
   \[
   2x + 24 = 30
   \]
   Subtracting 24 from both sides:
   \[
   2x = 6
   \]
   Dividing by 2:
   \[
   x = 3 \text{ cm}
   \]

So, the number that should go in the box is **3 cm**.

Would you like more details on any of the steps? Here are five related questions for practice:

1. How would the perimeter change if the unknown length was doubled?
2. What would be the area of this shape if all the dimensions were given?
3. How can you calculate the total width of the shape using the dimensions?
4. How would the problem change if the perimeter was 40 cm instead of 30 cm?
5. Can you write an equation for the area of the L-shape using algebra?

**Tip**: When dealing with shapes, it's always helpful to label every known and unknown length to ensure clarity while calculating perimeter or area.

The perimeter of this shape is 30 cm. What number should go in the box?

This problem explores the concept of perimeter with a composite shape, requiring the calculation of an unknown length given a total perimeter of 30 cm. It involves basic algebraic techniques and is suitable for middle school students (Grades 6-8).

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