Question

The area of a trapezium is $138m^2$. The distance and the difference between the lengths of the parallel sides are $12m$ and $7m$ respectively. Find the lengths of the parallel sides.

Answer 1

Area of the trapezium $=\frac{1}{2}\times \left(sumofparallelsides\right)\times h$
$138=\frac{1}{2}\times \left(sum\right)\times 12$
$sum=\frac{138}{6}=23$
$\therefore a+b=23-------\left(1\right)$
Now the difference is given,
$a-b=7-------\left(2\right)$
Adding equation (1) and (2)
$2a=30$
$a=15$
$\therefore b=8$