a cosine rule question

[neelam]

The diagonals of a parallelogram have lengths of 12cm and 18cm and the angle between them is 72 degrees. Find the lengths of the sides of the parallelogram. There is no diagram and I've been trying to find out the sides of the triangle created in the parallelogram so I can do the cosine rule to find the lengths, but I cant figure out how long the sides are of the triangles. I have drawn a diagram to make it clear. Any help will be appreciated.

 

[pka]

The diagonals of a parallelogram have lengths of 12cm and 18cm and the angle between them is 72 degrees. Find the lengths of the sides of the parallelogram. There is no diagram and I've been trying to find out the sides of the triangle created in the parallelogram so I can do the cosine rule to find the lengths, but I cant figure out how long the sides are of the triangles. I have drawn a diagram to make it clear. Any help will be appreciated.

The diagonals of a parallelogram bisect one another.
So now you the values of $\displaystyle p~\&~q$ in your second diagram.

Now use the cosine law: $\displaystyle c^2=a^2+b^2-2ab\cos(\theta)~.$