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.
Let the lengths of the parallel sides be $x \mathrm{~cm}$ and $2 x \mathrm{~cm}$.
Area of trapezium $=\left\{\frac{1}{2} \times(x+2 x) \times 84\right\} \mathrm{m}^{2}$
$=\left(\frac{1}{2} \times 3 x \times 84\right) \mathrm{m}^{2}$
$=(42 \times 3 x) \mathrm{m}^{2}$
$=126 x \mathrm{~m}^{2}$
Area of the trapezium $=9450 \mathrm{~m}^{2}$ (Given)
$\therefore 126 x=9450$
$\Rightarrow x=\frac{9450}{126}$
$\Rightarrow x=75$
Thus, the length of the parallel sides are $75 \mathrm{~m}$ and $150 \mathrm{~m}$, that is, $(2 \times 75) \mathrm{m}$, and the length of the longer side is $150 \mathrm{~m}$.