The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
• For the first option, the first two sides sum up to 7 (2 + 5) 7 is less than 10, then these cannot be the lengths of the sides of a triangle.
• When you sum up any two sides of the second option, you get a number that is greater than the third side, like this:
4 + 4 > 7, 8 > 7
4 + 7 > 4, 11 > 4
Then, the second option 4×4×7 is a possible group of lengths for a triangle
• For the third option 14×11×6 its also possible to prove that these lengths can represent a triangle, like this:
14 + 11 > 16, 25 > 16
11 + 6 > 14, 17 > 14
14 + 6 > 11, 20 > 11
• It is well known that there are triangles whose three sides have the same lengths (equilateral triangle) then there is no need to prove it, these lengths are possible for a triangle.
• These lengths can't be possible for a triangle, since 22 (2+20) is not greater than 24 (the third side).
Then only the second (4×4×7), the third (14×11×16) and the fourth (8×8×8) options are possible sides of a triangle.