Question

Construct two similar triangles, taking the measurement of your choice. Compare the perimeters of these two triangles and write your conclusion.

Answer 1

Let ΔABC and ΔPQR be two similar triangles. Then,

Let P₁ and P₂ be the perimeters of ΔABC and ΔPQR.

Let

P₁ = AB + BC + AC

⇒ P₁ = k PQ + k QR +k PR

⇒ P₁ = k (PQ + QR + PR)

P₂ = PQ + QR + PR

Thus, if two triangles are similar, then the ratio of their corresponding sides is same as the ratio of their corresponding perimeters.

If AB = 2 cm, BC = 3 cm and AC = 4 cm and, PQ = 6 cm, QR = 9 cm and PQ = 12 cm, then

Hence,