A field is in the shape of a parallelogram. The two adjacent sides are in the ratio 4:5. A fence 216 m long is placed along the boundary of the field. Find the sides of the parallelogram.

Answer

To solve the problem step by step, we will follow the given information about the parallelogram and the ratio of its sides.

### Step-by-Step Solution:

1. **Understand the Problem**: We have a parallelogram with two adjacent sides in the ratio of 4:5. We also know that the total length of the fence around the field (the perimeter) is 216 meters.

2. **Assign Variables**: Let the lengths of the two adjacent sides be represented as:
- Side 1 = 4x
- Side 2 = 5x
Here, x is a common multiplier.

3. **Calculate the Perimeter**: The perimeter (P) of a parallelogram is given by the formula:
\[ P = 2 \times (\text{Side 1} + \text{Side 2}) = 2 \times (4x + 5x) \]
Simplifying this, we get:
\[ P = 2 \times 9x = 18x \]

4. **Set Up the Equation**: Since we know the perimeter is 216 meters, we can set up the equation:
\[ 18x = 216 \]

5. **Solve for x**: To find the value of x, divide both sides of the equation by 18:
\[ x = \frac{216}{18} = 12 \]

6. **Find the Lengths of the Sides**:
- For Side 1 (4x):
\[ 4x = 4 \times 12 = 48 \text{ meters} \]
- For Side 2 (5x):
\[ 5x = 5 \times 12 = 60 \text{ meters} \]

7. **State the Sides of the Parallelogram**: The lengths of the sides of the parallelogram are:
- Side 1 = 48 meters
- Side 2 = 60 meters
- Since opposite sides are equal in a parallelogram, the other two sides are also 48 meters and 60 meters.

### Final Answer:
The sides of the parallelogram are 48 meters and 60 meters.