Question

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, find the two parallel sides.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{lengths}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{be}x\mathrm{cm}\mathrm{and}\left(x+6\right)\mathrm{cm}. \\ \mathrm{Now}, \\ \mathrm{Area}\mathrm{of}\mathrm{trapezium}=\left\{\frac{1}{2}\times \left(x\mathit{+}x\mathit{+}\mathit{6}\right)\times 9\right\}{\mathrm{cm}}^2 \end{gathered}$$
$$\begin{gathered} =\left(\frac{1}{2}\times \left(2x+6\right)\times 9\right){\mathrm{cm}}^2 \\ =4.5\left(2x+6\right){\mathrm{cm}}^2 \\ =\left(9x+27\right){\mathrm{cm}}^2 \end{gathered}$$

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{trapezium}=180{\mathrm{cm}}^2\left(\mathrm{Given}\right) \\ \therefore 9x+27=180 \\ \Rightarrow 9x=\left(180-27\right) \\ \Rightarrow 9x=153 \\ \Rightarrow x=\frac{153}{9} \\ \Rightarrow x=17 \\ \mathrm{Hence},\mathrm{the}\mathrm{lengths}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{are}17\mathrm{cm}\mathrm{and}23\mathrm{cm},\mathrm{that}\mathrm{is},\left(17+6\right)\mathrm{cm}. \end{gathered}$$