Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

(A) Yes,the two triangles are similar.
Let the sides of the first triangle be $a_1, b_1, c_1$ and its perimeter be $P_1 = a_1 + b_1 + c_1$.
Let the sides of the second triangle be $a_2, b_2, c_2$ and its perimeter be $P_2 = a_2 + b_2 + c_2$.
Given that $a_1 = 3a_2$,$b_1 = 3b_2$,and $P_1 = 3P_2$.
Since $P_1 = a_1 + b_1 + c_1$ and $P_2 = a_2 + b_2 + c_2$,we have $3P_2 = 3a_2 + 3b_2 + c_1$.
Substituting $P_2 = a_2 + b_2 + c_2$,we get $3(a_2 + b_2 + c_2) = 3a_2 + 3b_2 + c_1$,which simplifies to $3c_2 = c_1$.
Since all three corresponding sides are proportional $(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} = 3)$,by the $SSS$ similarity criterion,the two triangles are similar.