Question

The two parallel sides of a trapezium are in the ratio 3:5 and its height is 9 cm. What are the dimensions of the parallel sides of the trapezium if its area is 90 cm²?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{trapezium}\mathrm{are}3x\mathrm{and}5x. \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{trapezium}=9\mathrm{cm} \\ \mathrm{Area}\mathrm{of}\mathrm{trapezium}=90{\mathrm{cm}}^2 \\ \Rightarrow \frac{1}{2}\left(\mathrm{sum}\mathrm{of}\mathrm{parallel}\mathrm{sides}\right)\times \mathrm{height}=90 \\ \Rightarrow \frac{1}{2}\left(3x+5x\right)\times 9=90 \\ \Rightarrow \frac{1}{2}\times 8x\times 9=90 \\ \Rightarrow 4x\times 9=90 \\ \Rightarrow x=\frac{90}{36}=2.5 \\ \mathrm{So}, \\ \mathrm{smaller}\mathrm{parallel}\mathrm{side}=7.5\mathrm{cm} \\ \mathrm{Longer}\mathrm{parallel}\mathrm{side}=12.5\mathrm{cm} \end{gathered}$$