The ratio of the length of the parallel sides of a trapezium is 3:2. The shortest distance between them is 15 cm. If the area of the trapezium is `450 cm^(2)`, the sum of the length of the parallel sides is

Options

A. `15 cm`
B. `36 cm`
C. `42 cm`
D. `60 cm`

Answer

To solve the problem, we need to find the sum of the lengths of the parallel sides of the trapezium given the area and the height. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understand the formula for the area of a trapezium**:
The area \( A \) of a trapezium is given by the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
where \( a \) and \( b \) are the lengths of the parallel sides, and \( h \) is the height (the shortest distance between the parallel sides).

2. **Identify the given values**:
- Area \( A = 450 \, \text{cm}^2 \)
- Height \( h = 15 \, \text{cm} \)

3. **Substitute the known values into the area formula**:
\[ 450 = \frac{1}{2} \times (a + b) \times 15 \]

4. **Simplify the equation**:
First, multiply both sides by 2 to eliminate the fraction:
\[ 900 = (a + b) \times 15 \]
Now, divide both sides by 15:
\[ a + b = \frac{900}{15} \]

5. **Calculate \( a + b \)**:
\[ a + b = 60 \, \text{cm} \]

6. **Conclusion**:
The sum of the lengths of the parallel sides of the trapezium is \( 60 \, \text{cm} \).