Question

The difference between the lengths of the parallel sides of a trapezium is $8cm,$ the perpendicular distance between these sides is $24cm$ and the area of the trapezium is $312c{m}^2.$ Find the length of each of the parallel sides.

Answer 1

Let the length of the parallel side be $x$
The other parallel side is $x+8$ [$\because$ Difference between the parallel sides $=8cm$]
Given, Area of the trapezium $=312c{m}^2$ and the perpendicular distance $=24cm$

Area of the trapezium $=\frac{1}{2}\times$(Sum of parallel sides)$\times$(Perpendicular Distance between the parallel lines)
$312=\frac{1}{2}\{x+(x+8\left)\right\}\times \left(24\right)$
$\Rightarrow 312=12(2x+8)$
$\Rightarrow 2x+8=26$
$\Rightarrow 2x=18$
$\Rightarrow x=9cm$
$\therefore$ one parallel side $=x=9cm$
the other parallel side $=x+8=9+8=17cm$
The length of the parallel sides are $9cm$ and $17cm$.