Discussion
The perimeter and area of a trapezium are respectively 52 cm and 128 cm2. If the sum of its non-parallel sides is 20 cm, then the distance between its parallel sides is :
Answer: B
The distance between the parallel sides is 8 cm.
The perimeter is the sum of all four sides, so the two parallel sides add to \(52 - 20 = 32\) cm. Then use the area formula for a trapezium.
\[ \begin{aligned} \text{Area} &= \tfrac{1}{2} \times (\text{sum of parallel sides}) \times h \\ 128 &= \tfrac{1}{2} \times 32 \times h \\ h &= \frac{128}{16} = 8 \text{ cm} \end{aligned} \]
Using the whole perimeter, 52 cm, in place of the parallel sides gives a height of about 4.9 cm, and forgetting the half gives 4 cm; neither is offered, which confirms 8 cm.
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