Q. 14.1( 9 Votes )

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

Answer :

(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.


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