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

SOLUTION :  

(i)

Let a = 7 cm , b = 24 cm , c = 25 cm

Here, the larger side is c = 25 cm

c² = (25)² = 625

b² = (24)² = 576

a² = (7)² = 49

By Converse of Pythagoras theorem: In a triangle , if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the side is a right angle. (c² = a² + b²)

Here,

c² = a² + b²

625 =  49 + 576

625 =  625

Hence, the triangle with the given sides is a right angled triangle.

(ii)  

Let a = 9 cm , b = 16 cm , c = 18 cm

Here, the larger side is c = 18 cm

c² = (18)² = 324

b² = (16)² = 256

a² = (9)² = 81

By Converse of Pythagoras theorem: In a triangle , if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the side is a right angle. (c² = a² + b²)

Here,

c² ≠ a² + b²

324 ≠ 81 + 256

324 ≠  337

Hence, the triangle with the given sides is not a right angled triangle.

(iii)

Let a = 1.6 cm , b = 3.8 cm , c = 4 cm

Here, the larger side is c = 4 cm

c² = (4)² = 16

b² = (3.8)² = 14.44

a² = (1.6)² = 2.56

By Converse of Pythagoras theorem: In a triangle , if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the side is a right angle. (c² = a² + b²)

Here,

c² ≠ a² + b²

16 ≠  2.56 + 14.44

16 ≠  17

Hence, the triangle with the given sides is not a right angled triangle.

(iv)

Let a = 8 cm , b = 10 cm , c = 6 cm

Here, the larger side is b = 10 cm

c² = (6)² = 36

b² = (10)² = 100

a² = (8)² = 64

By Converse of Pythagoras theorem: In a triangle , if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the side is a right angle. (b² = a² + c²)

Here,

b² = a² + c²

100  =  64 + 36

100  = 100

Hence, the triangle with the given sides is a right angled triangle.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

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thanks

Step-by-step explanation:

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