Question

Triangle ABC has side of length 5, 6 and 7 units, while triangle PQR has a perimeter of 360 units when will ΔABC similar to ΔPQR? And hence find the sides of the triangle PQR.

Answer 1

Let AB = 5 units, BC = 6 units and AC = 7 units. Let P₁ and P₂ be the perimeters of ΔABC and ΔPQR.

P₁ = 5 + 6 + 7 = 18 units and P₂ = PQ + QR + PR = 360 units

Now, ΔABC and ΔPQR will be similar if the ratio of their corresponding sides is same as the ratio of their corresponding perimeters.

If ΔABC and ΔPQR are similar, then

Let ... (1)

P₁ = AB + BC + AC

⇒ P₁ = k PQ + k QR + k PR

⇒ P₁ = k (PQ + QR + PR)

P₂ = PQ + QR + PR

From (1) and (2), we have:

Thus, the side lengths of ΔPQR are 100 units, 120 units and 140 units.