Question

Mark (✓) against the correct answer:
The area of a trapezium is 384 cm². Its parallel sides are in the ratio 5 : 3 and the distance between them is 12 cm. The longer of the parallel sides is
(a) 24 cm
(b) 40 cm
(c) 32 cm
(d) 36 cm

Answer 1

(b) 40 cm

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{be}5x\mathrm{cm}\mathrm{and}3x\mathrm{cm},\mathrm{respectively}. \\ A\mathrm{rea}\mathrm{of}\mathrm{the}\mathrm{trapezium}=\left\{\frac{1}{2}\times \left(5x+3x\right)\times 12\right\}\mathrm{cm} \end{gathered}$$²
$=\left(\frac{1}{2}\times 8x\times 12\right)\mathrm{cm}$²=48x cm²

$$\begin{gathered} \mathrm{But},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{trapezium}is384{\mathrm{cm}}^2. \\ 48x=384 \\ \Rightarrow x=\frac{384}{48}=8 \\ L\mathrm{onger}\mathrm{side}=5\mathrm{x}=5\times 8=40\mathrm{cm} \end{gathered}$$