Question

The area of a trapezium is $279$ sq. cm and the distance between its two parallel sides is $18$ cm. If one of its parallel sides is longer than the other side by $5$ cm, find the value of smallest lengths of its parallel sides.

Answer 1

Let the lengths of the parallel sides of the trapezium be $acm$ and $a+5cm$

Area of a trapezium $=\frac{1}{2}\times \left(Sumofparallelsides\right)\times height$

$\Rightarrow \frac{1}{2}\times (a+a+5)\times 18cm=279{cm}^2$

$\Rightarrow \frac{1}{2}\times (2a+5)\times 18=279$

$2a+5=31$

$\Rightarrow a=13$

Hence, the lengths of the parallel sides of the trapezium are $a=13cm$ and $a+5=18cm$

Thus length of smallest parallel side is $13$ cm