Question

The parallel sides of a trapezium are in the ratio 3 : 4. If the distance between the parallel sides is 9 dm and its area is $126d{m}^2$, find the lengths of smallest its parallel sides.

Answer 1

Let the lengths of the parallel sides of the trapezium be $3a$ $dm$ and $4a$ $dm$

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

$=>\frac{1}{2}\times (3a+4a)\times 9dm=126{dm}^2$

$=>\frac{1}{2}\times 7a\times 9=126$

$=>a=4$

Hence, the lengths of the parallel sides of the trapezium are $3a=12dm$ and $4a=16dm$