Question

Tick (✓) the correct answer:
The area of a trapezium is 180 cm² and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, the length of the longer of the parallel sides is
(a) 17 cm
(b) 23 cm
(c) 18 cm
(d) 24 cm

Answer 1

(b) 23 cm

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{be}x\mathrm{cm}\mathrm{and}\left(x+6\right)\mathrm{cm},\mathrm{respectively}. \\ \mathrm{Then},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{trapezium}=\left\{\frac{1}{2}\times \left(x+x+6\right)\times 9\right\}{\mathrm{cm}}^2 \end{gathered}$$
$$\begin{gathered} =\left\{\frac{1}{2}\times \left(2x+6\right)\times 9\right\}{\mathrm{cm}}^2 \\ =4.5\left(2x+6\right){\mathrm{cm}}^2 \\ =\left(9x+27\right){\mathrm{cm}}^2 \end{gathered}$$
$$\begin{gathered} \mathrm{But}\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{trapezium}is180{\mathrm{cm}}^2. \\ \therefore 9x+27=180 \\ \Rightarrow 9x=\left(180-27\right) \\ \Rightarrow 9x=153 \\ \Rightarrow x=\frac{153}{9} \\ \Rightarrow x=17 \\ \mathrm{Therefore},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{are}17\mathrm{cm}\mathrm{and}\left(17+6\right)\mathrm{cm},\mathrm{which}\mathrm{is}\mathrm{equal}\mathrm{to}23\mathrm{cm}. \\ \mathrm{Hence},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{longer}\mathrm{parallel}\mathrm{side}\mathrm{is}23\mathrm{cm}. \end{gathered}$$