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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.

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    @OldJohn: thanks very much. Would you mind converting your comment as an answer?2012-06-14

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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.

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Suppose that your similar triangle has sides of length $x, y, z$. We'll then have, by similarity, $x=2t, y=3t, z=4t$, for some (positive) $t$. The perimeter, then, will be $2t+3t+4t = (2+3+4)t = 9t = 36$ so we have $t=4$ and so the sides will be $2\cdot4, 3\cdot4, 4\cdot4$ or $8, 12, 16.$