Find the missing number in the box in the following proportion:
`square : 8 : : 12 : 32 `

Answer

To find the missing number in the proportion `square : 8 : : 12 : 32`, we can set up the equation based on the concept of proportions.

### Step-by-Step Solution:

1. **Set Up the Proportion**:
We can express the proportion as:
\[ \frac{\text{square}}{8} = \frac{12}{32} \]
Let's denote the missing number (the value of "square") as \( x \). So we rewrite it as:
\[ \frac{x}{8} = \frac{12}{32} \]

2. **Cross-Multiply**:
To solve for \( x \), we can cross-multiply:
\[ x \cdot 32 = 12 \cdot 8 \]

3. **Calculate the Right Side**:
Now, calculate \( 12 \cdot 8 \):
\[ 12 \cdot 8 = 96 \]
So, we have:
\[ x \cdot 32 = 96 \]

4. **Solve for \( x \)**:
Now, divide both sides by 32 to isolate \( x \):
\[ x = \frac{96}{32} \]

5. **Perform the Division**:
Now, simplify \( \frac{96}{32} \):
\[ x = 3 \]

Thus, the missing number in the box is **3**.