Which of the following sets of numbers could not represent the three sides of a right triangle?

25, 32, 40 can not form a right angle triangle.

Step-by-step explanation:

By Pythagoras theorem,

⇒ (40)² = (25)² + (32)²

⇒ 1600 = 625 + 1024

⇒ 1600 ≠ 1689

option b

Step-by-step explanation:

according to the pythagoras theorem to be right angled triangle the sum of square of two smaller sides must be equal to the square of hypotenuse.

so ,

20 and 21 are smaller sides and hypotenuse be 29

pythagoras theorem

a^2 + b^2 = c^2

20^2 + 21^2 = 29^2

400 + 441 = 841

841 = 841  (since both sides are equal it forms right angled triangle)

25 and 32 are smaller sides and 40 be hypotenuse

a^2 + b^2 = c^2

25^2 + 32^2 = 40^2

625 + 1024 = 1600

1649 = 1600 (both sides are not equal so it does not form right angle triangle)

30 and 72 are smaller sides whereas 78 is hypotenuse

a^2 + b^2 = c^2

30^2 + 72^2 = 78^2

900 + 5184 = 6084

6084 = 6084 (since both sides are equal it forms right angled triangle )

32 and 60 are smaller sides and 68 is hypotenuse

a^2 + b^2 = c^2

32^2 + 60^2 = 68^2

1024 + 3600 = 4624

4624 = 4624  (since both sides are equal it forms right angled triangle )