Question

Tick (✓) the correct answer:
The parallel sides of a trapezium are in the ratio 3 : 4 and the perpendicular distance between them is 12 cm. If the area of the trapezium is 630 cm², then its shorter of the parallel sides is
(a) 45 cm
(b) 42 cm
(c) 60 cm
(d) 36 cm

Answer 1

(a) 45 cm

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{be}3\mathrm{x}\mathrm{cm}\mathrm{and}4\mathrm{x}\mathrm{cm},\mathrm{respectively}. \\ \mathrm{Then},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{trapezium}=\left\{\frac{1}{2}\times \left(3x+4x\right)\times 12\right\}{\mathrm{cm}}^2 \end{gathered}$$
$$\begin{gathered} =\left(\frac{1}{2}\times 7x\times 12\right)c{m}^2 \\ =42xc{m}^2 \end{gathered}$$

$\mathrm{But}\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{trapezium}is630{\mathrm{cm}}^2.$

$$\begin{gathered} \therefore 42x=630 \\ \Rightarrow x=\frac{630}{42} \\ \Rightarrow x=15cm \end{gathered}$$
$$\begin{gathered} L\mathrm{ength}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}=\left(3\times 15\right)\mathrm{cm}=45\mathrm{cm} \\ \left(4\times 15\right)\mathrm{cm}=60\mathrm{cm} \\ \mathrm{Hence},\mathrm{the}\mathrm{sho}\mathrm{rter}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{is}45\mathrm{cm}. \end{gathered}$$