Relationship between Perimeter of 2 Similar Triangle

Question

Is there any proof for the relation between perimeter of 2 similar triangles, like there is one for the area ? Pls help and tell if there is any proof ?

Answer 1

Hint:

If $ABC$ and $A'B'C'$ are similar triangles than, for some $k>0$ we have: $$ \overline{A'B'}=k \overline{AB}\qquad \overline{A'C'}=k \overline{AC}\qquad \overline{C'B'}=k \overline{CB} $$

so we can find the relation between the perimeters of the two triangles simply adding the sides.