Which three lengths could be the lengths of the sides of a triangle?

a. 12 cm, 5 cm, 17 cm

b. 10 cm, 15 cm, 24 cm

c. 9 cm, 22 cm, 11 cm

d. 21 cm, 7 cm, 6 cm

There's a rule where the the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side So, add the two smallest numbers of each triangle and see if it is greater than the biggest number:

A: 5 + 12 = 17, and the longest side is 17. 17 isn't more than 17, so the answer isn't A.

B: 10 + 15 = 25, and the longest side is 24. 25 is more than 24, so 'B' can be a triangle! We know this is an answer, but we should always check to see if any other answers work.

C: 9 + 11 = 20, and the longest side is 22. 20 isn't more than 22, so the answer isn't 'C'

D: 7 + 6 = 13, and the longest side is 21. 13 isn't more than 21, so the answer isn't 'D'

Answer 'B' is the only one that can  make a triangle, so it's the right answer!

Hope I helped, let me know if you have any questions :)

He only rule for if three lengths could be a triangle is the sum of the two smaller must be larger than the third, so 

12 cm, 5 cm, 17 cm 
12 and 5 makes 17... if you made a triangle look like this it would be a straight line, not a triangle. 

10 cm, 15 cm, 24 cm 
10 and 15 makes 25... this could be a triangle 

9 cm, 22 cm, 11 cm 
9 and 11 makes 20... this could not be a triangle. 

21 cm, 7 cm, 6 cm 
7 and 6 makes 13... not a triangle.