Parallel sides of a trapezium are 14 cm and 35 cm and the area is 1176 `cm^2`. What is the value of the distance (in cm) between parallel sides?

Options

A. 72
B. 96
C. 24
D. 48

Answer

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

\[ \text{Area} = \frac{1}{2} \times (L_1 + L_2) \times h \]

Where:
- \(L_1\) and \(L_2\) are the lengths of the parallel sides,
- \(h\) is the height (the distance between the parallel sides).

Given:
- \(L_1 = 14 \, \text{cm}\)
- \(L_2 = 35 \, \text{cm}\)
- Area = \(1176 \, \text{cm}^2\)

Step 1: Substitute the values into the area formula.

\[ 1176 = \frac{1}{2} \times (14 + 35) \times h \]

Step 2: Calculate \(L_1 + L_2\).

\[ L_1 + L_2 = 14 + 35 = 49 \]

Step 3: Substitute this sum back into the area formula.

\[ 1176 = \frac{1}{2} \times 49 \times h \]

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

\[ 2352 = 49 \times h \]

Step 5: Solve for \(h\) by dividing both sides by 49.

\[ h = \frac{2352}{49} \]

Step 6: Perform the division.

\[ h = 48 \, \text{cm} \]

Thus, the distance between the parallel sides of the trapezium is \(48 \, \text{cm}\).