2018 THREE(e)

The above shape is made from wire. It has both vertical and horizontal lines of symmetry.

The ends of the shape are at the vertices of a square with a side length of 10 cm, as shown in
the diagram above.

The length of the piece of wire through the centre of the shape is $x$ cm.

Find the value(s) of $x$ that enables the shape to be made with the minimum length of wire.
You do not need to prove that the length is a minimum.

*You must use calculus and show any derivatives that you need to find when solving this
problem.*