If the area of trapezium is `250m^(2)`, then the distance between the parallel sides of lengths 15 m and 10 m, is

Options

A. 18 m
B. 20 m
C. 22 m
D. 30 m

Answer

To find the distance between the parallel sides of a trapezium given the area and the lengths of the parallel sides, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Area of the trapezium (A) = 250 m²
- Length of the first parallel side (L1) = 15 m
- Length of the second parallel side (L2) = 10 m

2. **Use the Formula for the Area of a Trapezium:**
The formula for the area of a trapezium is given by:
\[ A = \frac{1}{2} \times (L1 + L2) \times h \]
where \( h \) is the height (distance between the parallel sides).

3. **Substitute the Known Values into the Formula:**
Plugging in the values we have:
\[ 250 = \frac{1}{2} \times (15 + 10) \times h \]

4. **Calculate the Sum of the Parallel Sides:**
\[ 15 + 10 = 25 \]
Now, substitute this back into the equation:
\[ 250 = \frac{1}{2} \times 25 \times h \]

5. **Multiply Both Sides by 2 to Eliminate the Fraction:**
\[ 500 = 25 \times h \]

6. **Solve for \( h \):**
Divide both sides by 25:
\[ h = \frac{500}{25} = 20 \]

7. **Conclusion:**
The distance between the parallel sides (height) is \( h = 20 \) m.

### Final Answer:
The distance between the parallel sides is **20 meters**.