Question

Two opposite sides of a parallelogram each have a length of `7`. If one corner of the parallelogram has an angle of `( pi)/3` and the parallelogram's area is `72`, how long are the other two sides?

Answer 1

Other two sides are `11.88`

Explanation:

Area of a parallelogram is given by `axxbxxsintheta`, where `a` and `b` are two sides of parallelogram and `theta` is angle included between them.

As here one pair of sides are `7` units, inclded angle is `pi/3` and area is `72`, we have

`7xxbxxsin(pi/3)=72` or `7xxbxxsqrt3/2=72`

Hence `b=(72xx2)/(7xxsqrt3)=(3xx24xx2)/(7xxsqrt3)=48sqrt3/7`

or `b=11.88`