If the area of trapezium is 250 `m^(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 when the area and the lengths of the parallel sides are given, we can use the formula for the area of a trapezium:

\[ \text{Area} = \frac{1}{2} \times (a + b) \times h \]

Where:
- \( a \) and \( b \) are the lengths of the parallel sides,
- \( h \) is the distance between the parallel sides (height).

Given:
- Area \( = 250 \, m^2 \)
- Length of one parallel side \( a = 15 \, m \)
- Length of the other parallel side \( b = 10 \, m \)

We need to find \( h \).

### Step 1: Substitute the known values into the area formula.

\[ 250 = \frac{1}{2} \times (15 + 10) \times h \]

### Step 2: Simplify the expression inside the parentheses.

\[ 15 + 10 = 25 \]

So the equation becomes:

\[ 250 = \frac{1}{2} \times 25 \times h \]

### Step 3: Simplify further.

\[ 250 = \frac{25}{2} \times h \]

### Step 4: Multiply both sides by 2 to eliminate the fraction.

\[ 500 = 25h \]

### Step 5: Divide both sides by 25 to solve for \( h \).

\[ h = \frac{500}{25} \]

### Step 6: Calculate the value of \( h \).

\[ h = 20 \]

Thus, the distance between the parallel sides is \( 20 \, m \).

### Final Answer:
The distance between the parallel sides of the trapezium is \( 20 \, m \).

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