A carpet 5 m. 20 cm. long and 3 m. 20 cm. broad, is to be surrounded by a lace. Find the length of lace required.

Answer

To find the length of lace required to surround the carpet, we need to calculate the perimeter of the carpet. The carpet is in the shape of a rectangle, and the formula for the perimeter (P) of a rectangle is given by:

\[ P = 2 \times ( \text{Length} + \text{Breadth} ) \]

### Step-by-step Solution:

1. **Convert Measurements to a Consistent Unit**:
- The length of the carpet is given as 5 m 20 cm.
- Convert this to meters:
\[ 5 \text{ m} + 20 \text{ cm} = 5 \text{ m} + \frac{20}{100} \text{ m} = 5 + 0.2 = 5.2 \text{ m} \]
- The breadth of the carpet is given as 3 m 20 cm.
- Convert this to meters:
\[ 3 \text{ m} + 20 \text{ cm} = 3 \text{ m} + \frac{20}{100} \text{ m} = 3 + 0.2 = 3.2 \text{ m} \]

2. **Calculate the Perimeter**:
- Now, substitute the length and breadth into the perimeter formula:
\[ P = 2 \times (5.2 \text{ m} + 3.2 \text{ m}) \]
- First, calculate the sum of the length and breadth:
\[ 5.2 + 3.2 = 8.4 \text{ m} \]
- Now, calculate the perimeter:
\[ P = 2 \times 8.4 \text{ m} = 16.8 \text{ m} \]

3. **Final Result**:
- The length of lace required to surround the carpet is:
\[ 16.8 \text{ m} \]

### Summary:
The length of lace required to surround the carpet is **16.8 meters**.