Question

In a trapezium-shaped field, one of the parallel sides is twice the other. If the area of the field is $9450m^2$ and the perpendicular distance between the two parallel sides of $84m$, find the length of the longer of the parallel sides.

Answer 1

Given:

In Trapezium, one of the parallel sides is twice the other

Let one side of the parallel side be $x$

$\Rightarrow$ Another side be $=2x$

distance between the two parallel sides is $84m$

Area of the field $=9450m^2$

Since, Area of the trapezium

$=\frac{1}{2}\times \text{Sum of the parallel sides}\times \text{Distance between the two parallel sides}$

$\Rightarrow \frac{1}{2}\times (x+2x)\times 84m=9450m^2$

$\Rightarrow 3x\times 42m=9450m^2$

$\Rightarrow x=\frac{9450m^2}{3\times 42m}$

$\Rightarrow x=75m$ [First side]

$\Rightarrow 2x=2\times 75m=150m$ [Second side]

So, the length of longer side is $150m$