The lengths of the parallel sides of a trapezium are 19 cm and 13 cm and its area is `128 cm^(2)`. The distance between the parallel sides is

Options

A. 9 cm
B. 7 cm
C. 8 cm
D. 12.5 cm

Answer

To find the distance between the parallel sides of the trapezium, we can use the formula for the area of a trapezium:

\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]

Where:
- \(\text{Base}_1\) and \(\text{Base}_2\) are the lengths of the parallel sides.
- \(\text{Height}\) is the distance between the parallel sides.

### Step-by-step Solution:

1. **Identify the given values:**
- Base 1 (\(b_1\)) = 19 cm
- Base 2 (\(b_2\)) = 13 cm
- Area = 128 cm²

2. **Calculate the sum of the bases:**
\[ b_1 + b_2 = 19 \, \text{cm} + 13 \, \text{cm} = 32 \, \text{cm} \]

3. **Substitute the values into the area formula:**
\[ 128 = \frac{1}{2} \times (32) \times h \]

4. **Simplify the equation:**
\[ 128 = 16h \]
(since \(\frac{32}{2} = 16\))

5. **Solve for \(h\):**
\[ h = \frac{128}{16} = 8 \, \text{cm} \]

### Final Answer:
The distance between the parallel sides of the trapezium is **8 cm**.

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