Here some set of lengths given. We have to find which set of lengths can not form a right triangle.
To check whether it is a right triangle or not we will use Pythagoras theorem. If it holds true then the set will form a right triangle and if it is not true then it will not form a right triangle.
The Pythagoras theorem is
, where c = hypotenuse which is the largest length of the sides, a and b are other two sides.
The first set is, 20mm, 48mm, 52mm.
So here c = 52 as it is the largest side. We can take a and b any of the lengths 20 and 48. By substituting the values we will get,
![52^2 = 20^2 + 48^2](https://tex.z-dn.net/?f=%2052%5E2%20%3D%2020%5E2%20%2B%2048%5E2%20)
![2704 = 400+2304](https://tex.z-dn.net/?f=%202704%20%3D%20400%2B2304%20)
![2704 = 2704](https://tex.z-dn.net/?f=%202704%20%3D%202704%20)
The Pythagoras theorem holds true here. So this set will form a right angled triangle.
The second set is, 10mm, 24mm, 26mm.
By substituting the values we will get,
![26^2 = 10^2 + 24^2](https://tex.z-dn.net/?f=%2026%5E2%20%3D%2010%5E2%20%2B%2024%5E2%20)
![676 = 100+ 576](https://tex.z-dn.net/?f=%20676%20%3D%20100%2B%20576%20)
![676 = 676](https://tex.z-dn.net/?f=%20676%20%3D%20%20676%20)
The Pythagoras theorem holds true here. So this set will form a right angled triangle.
The third set is, 11mm, 24mm, 26mm.
By substituting the values we will get,
![26^2 = 11^2+24^2](https://tex.z-dn.net/?f=%2026%5E2%20%3D%2011%5E2%2B24%5E2%20)
![676 = 121 + 576](https://tex.z-dn.net/?f=%20676%20%3D%20121%20%2B%20576%20)
![676 = 697](https://tex.z-dn.net/?f=%20676%20%3D%20697%20)
The Pythagoras theorem does not hold true here. So this set will not form a right angled triangle.
The fourth set is, 5mm, 12mm, 13mm.
By substituting the values we will get,
![13^2 = 5^2 + 12^2](https://tex.z-dn.net/?f=%2013%5E2%20%3D%205%5E2%20%2B%2012%5E2%20)
![169 = 25+144](https://tex.z-dn.net/?f=%20169%20%3D%2025%2B144%20)
![169 = 169](https://tex.z-dn.net/?f=%20169%20%3D%20169%20)
The Pythagoras theorem holds true here. So this set will form a right angled triangle.
We have got the required answer. Option C is correct here.