The area of a trapezium is ` 441 cm^(2) ` and the ratio of parallel sides is 5:9. Also the perpendicular distance between them is 21 cm, the longer of parallel sides is :

Options

A. 36 cm
B. 27 cm
C. 18 cm
D. 28 cm

Answer

To find the longer of the parallel sides of the trapezium, we can follow these steps:

### Step 1: Understand the given information
We know that:
- The area of the trapezium is \( 441 \, \text{cm}^2 \).
- The ratio of the parallel sides is \( 5:9 \).
- The height (perpendicular distance between the parallel sides) is \( 21 \, \text{cm} \).

### Step 2: Assign variables to the parallel sides
Let the lengths of the parallel sides be:
- The shorter parallel side = \( 5x \)
- The longer parallel side = \( 9x \)

### Step 3: Use the area formula for a trapezium
The formula for the area \( A \) of a trapezium is given by:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the parallel sides, and \( h \) is the height.

Substituting the known values into the formula:
\[ 441 = \frac{1}{2} \times (5x + 9x) \times 21 \]

### Step 4: Simplify the equation
Combine the terms inside the parentheses:
\[ 441 = \frac{1}{2} \times (14x) \times 21 \]
Now simplify:
\[ 441 = 7x \times 21 \]
\[ 441 = 147x \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 147:
\[ x = \frac{441}{147} \]
Calculating this gives:
\[ x = 3 \]

### Step 6: Find the lengths of the parallel sides
Now we can find the lengths of the parallel sides:
- Shorter parallel side = \( 5x = 5 \times 3 = 15 \, \text{cm} \)
- Longer parallel side = \( 9x = 9 \times 3 = 27 \, \text{cm} \)

### Step 7: Conclusion
The longer of the parallel sides is:
\[ \text{Longer parallel side} = 27 \, \text{cm} \]