6/2, 2025 one interesting question that has nice solution : Beginning level

 

2010 Mathcounts Nationals sprint :

22. Side AB of regular hexagon ABCDEF is extended past B to point X such that AX = 3AB. Given that each side of the hexagon is 2 units long, what is the length of segment FX? Express your answer in simplest radical form.

Try this question first before you scroll down for the solution. 

Then when we draw line FX, and by the Pythagorean Theorem, we have $$FX = \sqrt{(\sqrt{3})^2 + (1 + 2 + 4)^2} = \sqrt{3 + 49} = \boxed{2\sqrt{13}}.$$