The area of a field in the shape of trapezium measures 1440 `m^(2)`. The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is 5 : 3, the length of the longer parallel side is :

Options

A. 45 m
B. 60 m
C. 75 m
D. 120 m

Answer

To solve the problem step by step, we will use the information provided in the question regarding the trapezium.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Area of the trapezium (A) = 1440 m²
- Perpendicular distance (height, h) between the parallel sides = 24 m
- Ratio of the parallel sides = 5:3

2. **Let the Lengths of the Parallel Sides be Defined**:
- Let the longer parallel side be \( 5x \) and the shorter parallel side be \( 3x \).

3. **Use the Area Formula for a Trapezium**:
The area \( A \) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the parallel sides, and \( h \) is the height.
Substituting the values:
\[ 1440 = \frac{1}{2} \times (5x + 3x) \times 24 \]

4. **Simplify the Equation**:
Combine the terms inside the parentheses:
\[ 1440 = \frac{1}{2} \times (8x) \times 24 \]
This simplifies to:
\[ 1440 = 4x \times 24 \]
\[ 1440 = 96x \]

5. **Solve for \( x \)**:
Divide both sides by 96:
\[ x = \frac{1440}{96} \]
Simplifying this gives:
\[ x = 15 \]

6. **Find the Length of the Longer Parallel Side**:
Now, substitute \( x \) back into the expression for the longer parallel side:
\[ \text{Longer parallel side} = 5x = 5 \times 15 = 75 \text{ m} \]

### Final Answer:
The length of the longer parallel side is **75 m**.