Question

The sides of certain triangles are given below. Determine which of them are right triangles.

(i) a = 7 cm, b = 24 cm and c = 25 cm 

(ii) a = 9 cm, b = 16 cm and c = 18 cm 

(iii) a = 1.6 cm, b = 3.8 cm and c = 4 cm 

(iv) a = 8 cm, b = 10 cm and c = 6 cm

Answer 1

(i) Given, 

a = 7 cm, b = 24 cm and c = 25 cm 

∴ a² = 49, b² = 576 and c² = 625 

Since, a² + b² = 49 + 576 = 625 = c² 

Then, by converse of Pythagoras theorem 

The given sides are of a right triangle. 

(ii) Given, 

a = 9 cm, b = 16 cm and c = 18 cm 

∴ a² = 81, b² = 256 and c² = 324 

Since, a² + b² = 81 + 256 = 337 ≠ c² 

Then, by converse of Pythagoras theorem 

The given sides cannot be of a right triangle. 

(iii) Given, 

a = 1.6 cm, b = 3.8 cm and C = 4 cm 

∴ a² = 2.56, b² = 14.44 and c² = 16 

Since, a² + b² = 2.56 + 14.44 = 17 ≠ c² 

Then, by converse of Pythagoras theorem 

The given sides cannot be of a right triangle. 

(iv) Given, 

a = 8 cm, b = 10 cm and C = 6 cm 

∴ a² = 64, b² = 100 and c² = 36 

Since, a² + c² = 64 + 36 = 100 = b² 

Then, by converse of Pythagoras theorem 

The given sides are of a right triangle