Discussion
The area of a trapezium is 384 sq. cm. Its parallel sides are in the ratio 3:5, and the perpendicular distance between them is 12 cm. Then the lengths of the parallel sides (bases) of the trapezium are :
Answer: A
The parallel sides are 24 cm and 40 cm.
Let the parallel sides be \(3k\) and \(5k\). The area of a trapezium is half the sum of the parallel sides times the height:
\[ \begin{aligned} \tfrac{1}{2}(3k + 5k) \times 12 &= 384 \\ 48k &= 384 \\ k &= 8 \end{aligned} \]
So the sides are \(3 \times 8 = 24\) cm and \(5 \times 8 = 40\) cm. The other pairs are not in the ratio 3:5 (12 and 18 is 2:3, 15 and 20 is 3:4), or do not give an area of 384.
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