A field is in the form of a trapezium.

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 $38 \mathrm{~m}$

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