Discussion
In trapezium PQRS, PQ || SR and the ratio of PQ to SR is 3:2. If the area of the trapezium is 480 cm2 and the distance between PQ and SR is 12 cm, then the length of SR is
Answer: B
The length of SR is 32 cm.
Let \(PQ = 3x\) and \(SR = 2x\). The area of a trapezium is half the sum of the parallel sides times the distance between them.
\[ \begin{aligned} \tfrac{1}{2}(3x + 2x) \times 12 &= 480 \\ 30x &= 480 \\ x &= 16 \end{aligned} \]
So \(SR = 2x = 32\) cm and \(PQ = 48\) cm. Check: \(\frac{1}{2}(48 + 32) \times 12 = 480\).
48 cm is PQ, the longer side. With SR = 24 cm the sides would be 36 and 24 and the area only 360 cm2; with SR = 36 cm the area would be 540 cm2.
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