Can't figure this one out.
The answer must be in exact value.
*Picture has been fixed to add the missing side length
You're expected to be able to recognise triangles that are of dimensions $\displaystyle (1, 1, \sqrt{2})$ and $\displaystyle (1, \sqrt{3}, 2)$.
Looking at the large triangle, its dimensions are
$\displaystyle (x, \sqrt{3}\,x, 2x)$.
So the base of this shape is $\displaystyle \sqrt{3}\,x$.
Using that information, you should be able to see that
$\displaystyle \sqrt{3}\,x - x = 4$
$\displaystyle x(\sqrt{3} - 1) = 4$
$\displaystyle x = \frac{4}{\sqrt{3} - 1}$
$\displaystyle x = \frac{4(\sqrt{3} + 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)}$
$\displaystyle x = \frac{4(\sqrt{3} + 1)}{3 - 1}$
$\displaystyle x = \frac{4(\sqrt{3} + 1)}{2}$
$\displaystyle x = 2(\sqrt{3} + 1)$
$\displaystyle x = 2\sqrt{3} + 2$.