Question

Two opposite sides of a parallelogram each have a length of `9`. 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

The length of other two sides are `9.24(2dp)`.

Explanation:

Let ABCD be the parallelogram having sides `AB=CD=9 and /_A=pi/3=60^0` Let a perpendicular from point D is drawn on side AB touches at point E. We know area of parallelogram is product of side AB and altitude DE. `:.72=9*DE or DE=8`. Now in `triangle DAE ; (DE)/(AD)=sin60 or AD=8/sin60=9.24(2dp)=BC`[Ans]