In a trapezium-shaped field, one of the parallel sides is twice the other. If the area of the field is `9450 m^(2)` and the perpendicular distance between the two parallel sides is 84 m, find the length of the longer of the parallel sides.

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the variables
Let the length of the shorter parallel side be \( x \) meters. Therefore, the length of the longer parallel side will be \( 2x \) meters, as given in the problem.

### Step 2: Write the formula for the area of a trapezium
The area \( A \) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the parallel sides, and \( h \) is the height (perpendicular distance between the parallel sides).

### Step 3: Substitute the known values into the formula
From the problem, we know:
- Area \( A = 9450 \, m^2 \)
- Height \( h = 84 \, m \)
- The lengths of the parallel sides are \( x \) and \( 2x \).

Substituting these values into the area formula gives:
\[ 9450 = \frac{1}{2} \times (x + 2x) \times 84 \]

### Step 4: Simplify the equation
This simplifies to:
\[ 9450 = \frac{1}{2} \times (3x) \times 84 \]
\[ 9450 = \frac{3x \times 84}{2} \]
\[ 9450 = 42 \times 3x \]

### Step 5: Solve for \( x \)
Now, we can isolate \( x \):
\[ 9450 = 126x \]
\[ x = \frac{9450}{126} \]
Calculating this gives:
\[ x = 75 \]

### Step 6: Find the length of the longer parallel side
Now that we have \( x \), we can find the longer parallel side:
\[ \text{Longer side} = 2x = 2 \times 75 = 150 \, m \]

### Final Answer
The length of the longer parallel side is \( 150 \, m \).

---