Question

The area of a trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. If the length of one of the parallel sides is 84 cm, then find the length of other parallel side.

• A. 38 cm
• B. 23 cm
• C. 25 cm
• D. 42 cm

Answer 1

The correct option is A 38 cm

Area of trapezium
= $\frac{1}{2}\times (a+b)\times h$,
where $a$ and $b$ are the lengths of the parallel sides and $h$ stands for the perpendicular distance between the parallel sides.

$\Rightarrow \frac{1}{2}\times (84+b)\times 26=1586{\text{cm}}^2$

$\Rightarrow (84+b)\times 13=1586$

$\Rightarrow (84+b)=\frac{1586}{13}=122$

$\Rightarrow b=122-84$

$\therefore b=38cm$

So, the length of the other parallel side is 38 cm.