Question

Two opposite sides of a parallelogram each have a length of `3`. If one corner of the parallelogram has an angle of `(3 pi)/4` and the parallelogram's area is `24`, how long are the other two sides?

Answer 1

`8sqrt2`

Explanation:

Let ABCD be the parallelogram as shown in the figure, with side AB=CD= 3. Let the other two sides AD and BC be equal to 'b'

Draw a perpendicular CE from C on to the extended side DE. If h is the height then DE would also be same as the height. Applying Pythagoras theorem to the rt. triangle CDE , `2h^2=9`. Hence `h=3/sqrt2`.

Area of ABCD would be base x height =bh=24.

This would give `b= 24/ h= 24/(3/sqrt2)= 8sqrt2`