Q:

A question about similar triangles.

Please, I would like help in solving this problem:  The sides of a triangle measure 2,3 and 4 cm respectively. The perimeter of a similar triangle is 36 cm. I want to find the length of each side of the second triangle.  
I did this by trial and error and I got the sides to 8, 12 and 16. I would like to know how to arrive at the answer formally.   
thanks.

A:

The sides of the second triangle must be $2a$, $3a$ and $4a$, and they must add up to 36, so:
$$2a + 3a + 4a = 36,$$
then $9a = 36$, and so $a=4$, giving sides 8, 12, 16.

