The area of a trapezium is 200 cm ^2 . Its parallel sides are in the ratio 2 : 3 and the perpendicular…

1. Analyze the Question

We are given:

• Area of the trapezium ($A$) = $200 \text{ cm}^2$
• Ratio of the parallel sides ($a : b$) = $2 : 3$
• Perpendicular distance (height, $h$) = $16 \text{ cm}$
• We need to find the actual lengths of the two parallel sides.

2. Explain the Concept

The formula for the area of a trapezium is:

Where:

• $a$ and $b$ are the lengths of the parallel sides.
• $h$ is the perpendicular height.

Since the sides are in a ratio of $2:3$, we can represent them as $2x$ and $3x$, where $x$ is a common multiplier.

3. Show the Solution

Step 1: Substitute the known values into the formula.

Step 2: Simplify the equation.

Step 3: Solve for $x$.

Step 4: Calculate the lengths of the sides.

• Side $a = 2x = 2 \times 5 = 10 \text{ cm}$
• Side $b = 3x = 3 \times 5 = 15 \text{ cm}$

4. Identify the Answer

The lengths of the parallel sides are $10 \text{ cm}$ and $15 \text{ cm}$. This corresponds to option A.

5. Exam Tip

When you are given a ratio in geometry problems, always introduce a constant (like $x$ or $k$). It makes the algebra much easier to manage. Also, always double-check your final answer by plugging it back into the area formula: $\frac{1}{2}(10 + 15) \times 16 = \frac{1}{2}(25) \times 16 = 25 \times 8 = 200$. It matches perfectly!