Question

The ratio of the lengths of the parallel sides of a trapezium is $4:1$. The distance between them is $10cm$. If the area of the trapezium is $500c{m}^2$. Find the lengths of the parallel sides

Answer 1

Area of the trapezium $=500c{m}^2$
Distance between the parallel sides of the trapezium $=10cm$
Ratio of the lengths of the parallel sides of the trapezium $=4:1$
Let the lengths of the parallel sides of the trapezium be $4x$ and $xcm$.
Area of the trapezium $=\frac{1}{2}(a+b)\times h$
$\Rightarrow 500=\frac{1}{2}(x+4x)\times 10$
$\Rightarrow 500=(x+4x)5$
$\Rightarrow 500=25x$
$\Rightarrow x=\frac{500}{25}=20cm$
$\therefore$ One parallel side $=20cm$
$\therefore$ The other parallel side $=4x=4\times 20=80cm$ ($\because$ parallel sides are in $4:1$)