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.
Solution:
Let the length of the required side be $x \mathrm{~cm}$.
Now,
Area of trapezium $=\left\{\frac{1}{2} \times(84+x) \times 26\right\} \mathrm{m}^{2}$
$=(1092+13 x) \mathrm{m}^{2}$
Area of trapezium $=1586 \mathrm{~m}^{2}$ (Given)
$\therefore 1092+13 x=1586$
$\Rightarrow 13 x=(1586-1092)$
$\Rightarrow 13 x=494$
$\Rightarrow x=\frac{494}{13}$
$\Rightarrow x=38 \mathrm{~m}$
Hence, the length of the other side is $38 \mathrm{~m}$