Find the fourth proportional to :
3 hrs 12 min, 24 min, 1 m 68 cm

Answer

To find the fourth proportional to the given terms: 3 hours 12 minutes, 24 minutes, and 1 meter 68 centimeters, we will follow these steps:

### Step 1: Convert all measurements to the same unit
First, we need to convert all the time and length measurements into a consistent unit.

- **Convert 3 hours 12 minutes to minutes:**
\[ 3 \text{ hours} = 3 \times 60 \text{ minutes} = 180 \text{ minutes} \]
\[ \text{Total} = 180 \text{ minutes} + 12 \text{ minutes} = 192 \text{ minutes} \]

- **The second term is already in minutes:**
\[ 24 \text{ minutes} \]

- **Convert 1 meter 68 centimeters to centimeters:**
\[ 1 \text{ meter} = 100 \text{ centimeters} \]
\[ \text{Total} = 100 \text{ centimeters} + 68 \text{ centimeters} = 168 \text{ centimeters} \]

### Step 2: Set up the proportion
Now we have:
- First term = 192 minutes
- Second term = 24 minutes
- Third term = 168 centimeters
- Fourth term = \( x \) (which we need to find)

The proportion can be set up as:
\[ \frac{192}{24} = \frac{168}{x} \]

### Step 3: Solve for \( x \)
Cross-multiply to solve for \( x \):
\[ 192 \cdot x = 24 \cdot 168 \]

Calculate \( 24 \cdot 168 \):
\[ 24 \cdot 168 = 4032 \]

Now, we have:
\[ 192x = 4032 \]

To find \( x \), divide both sides by 192:
\[ x = \frac{4032}{192} \]

Calculating \( \frac{4032}{192} \):
\[ x = 21 \]

### Conclusion
The fourth proportional is:
\[ \boxed{21} \]

---