Question

The area of a trapezium is 216 m² and its height is 12 m. If one of the parallel sides is 14 m less than the other, find the length of each of the parallel sides.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{be}\mathrm{x}\mathrm{m}\mathrm{and}\left(x-14\right)\mathrm{m}. \\ \mathrm{Then},\mathrm{area}\mathrm{of}\mathrm{the}t\mathrm{rapezium}=\left\{\frac{1}{2}\times \left(x+x-14\right)\times 12\right\}{\mathrm{m}}^2 \end{gathered}$$
$$\begin{gathered} =6\left(2x-14\right)m^2 \\ =\left(12x-84\right)m^2 \end{gathered}$$
$$\begin{gathered} \mathrm{But}\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{trapezium}is216{\mathrm{m}}^2. \\ \therefore 12x-84=216 \\ \Rightarrow 12x=\left(216+84\right) \\ \Rightarrow 12x=300 \\ \Rightarrow x=\frac{300}{12} \\ \Rightarrow x=25\mathrm{Hence},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{are}25\mathrm{m}\mathrm{and}\left(25-14\right)\mathrm{m},\mathrm{which}\mathrm{is}\mathrm{equal}\mathrm{to}11\mathrm{m}. \end{gathered}$$