Discussion
The lengths of the parallel sides of a trapezium are 11 cm and 25 cm and the distance between them is 12 cm. Its area is equal to the area of a rectangle whose sides are in the ratio 3 : 2. What is the perimeter (in cm) of the rectangle ?
Answer: C
The perimeter of the rectangle is 60 cm.
\[ \begin{aligned} \text{trapezium area} &= \tfrac{1}{2}(11 + 25) \times 12 = 216 \\ 3k \times 2k &= 6k^{2} = 216 \Rightarrow k = 6 \end{aligned} \]
The rectangle's sides are 18 cm and 12 cm, so its perimeter is 2(18 + 12) = 60 cm. 40, 50 and 70 do not correspond to a 3 : 2 rectangle of area 216 cm2.
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