Length spaces in $\mathbb{R}^{n}$

Question

I am presently reading the following notes: https://people.math.ethz.ch/~afigalli/lecture-notes-pdf/Optimal-Transport-and-Curvature.pdf and I could not fully understand the second part of Example 1.1, i.e:

If $X$ is a closed subset of $\mathbb{R}^{n}$ then $(X, d)$ is a length space if and only if X is convex.

Thanks for helping me on this point.