Could 10.5 cm, 8.0 cm, and 4,0 cm be the side lengths of a triangle?

Let’s use the basis that a 3:4:5 triangle would work.

Let’s multiply that ratio by 2.

6:8:10

A 10.5:8:4 triangle wouldn’t work because only one length matches.

An easier method:

Add 8 and 4 to get 12.

10.5 < 12, so it is not possible to make a triangle