# What is the length of the diagonal of a parallelogram of equal opposite sides?

As for example the two end sides are length 3 and the top and bottom are 7. Can we find a formula that will give us the length of the diagonal?

• I think there are many parallelograms like this. – pjs36 Mar 27 '17 at 16:26

Otherwise you have a non-rigid shape that can collapse towards the limit of a straight line twice traversed, whilst remaining a parallelogram. So you can only put limits on the size of the diagonals using the triangle inequality: $7-3<d<7+3$
However if you're given the measure of an angle between two of the sides, you can use the Law of Cosines $$c^2 = a^2 + b^2 - 2ab\cos \gamma$$ Where $a,b$ are sides of your parallelogram that intersect, $c$ is your diagonal, and $\gamma$ is the angle opposite $c$.