(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√2a 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.