Sides of some triangles are given below. Determine which of them are right triangles

(i) 8 cm, 15 cm, 17 cm

(ii) (2a —1) cm, cm and (2a + 1) cm

(iii) 7 cm, 24 cm, 25 cm

(iv) 1.4 cm, 4.8 cm, 5 cm

(i) Using Pythagoras theorem, i.e. if the square of the hypotenuse is equal to the sum of the other two sides. Then, the given triangle is a right angled triangle, otherwise not.

Here, (8)² + (15)² = 64 + 225 = 289 = (17)²

∴ given sides 8cm, 15cm and 17cm make a right angled triangle.

(ii) Using Pythagoras theorem, i.e. if the square of the hypotenuse is equal to the sum of the other two sides. Then, the given triangle is a right angled triangle, otherwise not.

Here, (2a – 1)² + (2√(2a))²

⇒ 4a² + 1 – 4a + 8a

⇒ 4a² + 1 + 4a

= (2a + 1)²

∴ given sides (2a —1) cm, 2 cm and (2a + 1) cm make a right angled triangle.

(iii) Using Pythagoras theorem, i.e. if the square of the hypotenuse is equal to the sum of the other two sides. Then, the given triangle is a right angled triangle, otherwise not.

Here, (7)² + (24)² = 49 + 576 = 625 = (25)²

∴ given sides 7cm, 24cm and 25cm make a right angled triangle.

(iv) Using Pythagoras theorem, i.e. if the square of the hypotenuse is equal to the sum of the other two sides. Then, the given triangle is a right angled triangle, otherwise not.

Here, (1.4)² + (4.8)² = 1.96 + 23.04 = 25 = (5)²

∴ given sides 1.4cm, 4.8cm and 5cm make a right angled triangle.