Question

Tick (✓) the correct answer:
The lengths of the parallel sides of a trapezium are 19 cm and 13 cm and its area is 128 cm². The distance between the parallel sides is
(a) 9 cm
(b) 7 cm
(c) 8 cm
(d) 12.5 cm

Answer 1

(c) 8 cm

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{be}\mathrm{x}\mathrm{cm}. \\ \mathrm{Then},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{trapezium}=\left\{\frac{1}{2}\times \left(19+13\right)\times \mathrm{x}\right\}{\mathrm{cm}}^2 \end{gathered}$$
$$\begin{gathered} =\left(\frac{1}{2}\times 32\times x\right){\mathrm{cm}}^2 \\ =16x{\mathrm{cm}}^2 \end{gathered}$$
$\mathrm{But}\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{trapezium}\mathrm{is}128{\mathrm{cm}}^2.$
$$\begin{gathered} \therefore 16x=128 \\ \Rightarrow x=\frac{128}{16} \\ \Rightarrow x=8\mathrm{cm} \end{gathered}$$