Half a triangle

A man wants to draw a line onto a perfectly equilateral triangle of paper. The line must leave an equal area each side of it. The lengths of the sides of the triangle are 10cm. All the man has is a piece of string, a pin and a pencil.

To draw the line, he pins one end of the string to a corner of the triangle with the other end attached to the pencil. He then moves the pencil in the shape of an arc to split the area in half.

How long is the string in cm to one decimal place?

Assume that the length of the string is exactly the same as the distance from the corner to the line.