If the thickness of a pile of 12 cardboards is 65 mm, find the thickness of a pile of 312 such cardboards.

Answer

To solve the problem step by step, we will use the concept of direct proportion.

### Step-by-Step Solution:

1. **Understand the relationship**: We know that the thickness of the cardboards is directly proportional to the number of cardboards. This means that if the number of cardboards increases, the thickness also increases.

2. **Identify the given values**:
- Thickness of 12 cardboards = 65 mm
- Number of cardboards we want to find the thickness for = 312

3. **Find the thickness of one cardboard**:
To find the thickness of one cardboard, we divide the total thickness by the number of cardboards:
\[ \text{Thickness of 1 cardboard} = \frac{65 \text{ mm}}{12} = \frac{65}{12} \text{ mm} \]

4. **Calculate the thickness of 312 cardboards**:
Now, we multiply the thickness of one cardboard by the number of cardboards (312):
\[ \text{Thickness of 312 cardboards} = \left(\frac{65}{12} \text{ mm}\right) \times 312 \]

5. **Simplify the calculation**:
\[ = \frac{65 \times 312}{12} \]
First, calculate \( 312 \div 12 \):
\[ 312 \div 12 = 26 \]
Now, multiply:
\[ 65 \times 26 = 1690 \text{ mm} \]

6. **Final answer**:
Thus, the thickness of a pile of 312 cardboards is **1690 mm**.