Question

In a trapezium-shaped field, one of the parallel sides is twice the other. If the area of the field is 9450 m² and the perpendicular distance between the two parallel sides is 84 m, find the length of the longer of the parallel sides.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{lengths}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{be}\mathit{}x\mathrm{cm}\mathrm{and}2x\mathrm{cm}. \\ \mathrm{Area}\mathrm{of}\mathrm{trapezium}=\left\{\frac{1}{2}\times \left(x+2x\right)\times 84\right\}{\mathrm{m}}^2 \end{gathered}$$
$$\begin{gathered} =\left(\frac{1}{2}\times 3x\times 84\right){\mathrm{m}}^2 \\ =\left(42\times 3x\right){\mathrm{m}}^2 \\ =126x{\mathrm{m}}^2 \end{gathered}$$

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{trapezium}=9450{\mathrm{m}}^2\left(\mathrm{Given}\right) \\ \therefore 126x=9450 \\ \Rightarrow x=\frac{9450}{126} \\ \Rightarrow x=75 \\ \mathrm{Thus},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{are}75\mathrm{m}\mathrm{and}150\mathrm{m},\mathrm{that}\mathrm{is},\left(2\times 75\right)\mathrm{m},\mathrm{and}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{longer}\mathrm{side}\mathrm{is}150\mathrm{m}. \end{gathered}$$