# 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

## 2 Answers

If the two diagonals are equal, you have a rectangle and the length of the diagonal can be obtained using the Pythagorean theorem.

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: $7-3<d<7+3$

Note that all parallelograms have equal opposite sides.

As noted in the other answers, the parallelogram you described is not unique.

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 $c$.