# Prove that if two triangles are similar then the ratio of their perimeters is equal to the ratio of the corresponding sides

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by 2092000

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by 2092000

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So

Let the ratio of sides =

We need to show that the ratio of perimeters is also x.

perimeter of ΔABC = AB+BC+AC

perimeter of ΔPQR = PQ+QR+PR

So perimeter of ΔABC = x.PQ + x.PR + x.QR = x(PQ+PR+QR)

ratio of perimeters =

⇒ Ratio =

Proved.