Question

Two opposite sides of a parallelogram each have a length of `18`. If one corner of the parallelogram has an angle of `( pi)/3` and the parallelogram's area is `54`, how long are the other two sides?

Answer 1

The length of other two sides are `3.46` unit each.

Explanation:

Let ABCD be the paralellogram of which opposite sides `AB=CD=18` and `/_ A=pi/3=60^0` and DE (altitude) is perpendicular from D on AB. We know Area of paralellogram = `AB*DE=54 or DE= 54/18=3` Now ADE is a right angled triangle of which AD is hypotenuse.`:.sin 60=(DE)/(AD) or sin60=3/(AD) or AD=3/sin60=3/((sqrt3)/2)=3.46 (2dp)=BC`[Ans]