Question

A field is in the form of a trapezium. Its area is 1586 m² and the distance between its parallel sides is 26 m. If one of the parallel sides is 84 m, find the other.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{required}\mathrm{side}\mathrm{be}x\mathrm{cm}. \\ \mathrm{Now}, \\ \mathrm{Area}\mathrm{of}\mathrm{trapezium}=\left\{\frac{1}{2}\times \left(84+x\right)\times 26\right\}{\mathrm{m}}^2 \end{gathered}$$

$=\left(1092+13x\right){\mathrm{m}}^2$

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{trapezium}=1586{\mathrm{m}}^2\left(\mathrm{Given}\right) \\ \therefore 1092+13x=1586 \\ \Rightarrow 13x=\left(1586-1092\right) \\ \Rightarrow 13x=494 \\ \Rightarrow x=\frac{494}{13} \\ \Rightarrow x=38\mathrm{m} \\ \mathrm{Hence},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{other}\mathrm{side}\mathrm{is}38\mathrm{m}. \end{gathered}$$