Shortest arm

In any triangle, the shortest side always lies opposite to the smallest interior angle.

So, in $\triangle ABE$ , the shortest side is $BE$ .

Likewise, in $\triangle BCE$ , the shortest side is $CE$ , and in $\triangle CDE$ the shortest side is $DE$ .

That tells us that $BE>CE>DE$ , and thus $DE$ is the shortest of all arms.

In Triangle ABE, The shortest side is BE (By Triangle Inequality). In Triangle BCE, The shortest side is BC (By Triangle Inequality). Therefore,BC<BE. And, in Triangle CED, The shortest side side is DE (By Triangle Inequality). Hence,DE<BC and is the shortest side.