Similar triangles have perimeters in ratio k

Dependencies: AA similarity (for the definition of the similarity ratio).

Statement

Suppose $\triangle ABC \sim \triangle A'B'C'$ with similarity ratio $k$ (i.e. $AB / A'B' = BC / B'C' = CA / C'A' = k$). Let $P = AB + BC + CA$ and $P' = A'B' + B'C' + C'A'$ denote the perimeters of the two triangles. Then

In other words, the perimeters of similar triangles are in the same ratio as the similarity ratio.