If the lengths of two sides f a triangle are 2 and 5 , the length of the third side could be
1) 1
2) 6
3) 2
4) 7

Question

If the lengths of two sides f a triangle are 2 and 5 , the length of the third side could be 
1) 1
2) 6
3) 2 
4) 7

wolf1728 · Answer

choice 2 - six

wolf1728 · Answer

The third side must be less than 7 and greater than 3. http://1728.org/trianinq.htm

anonymous · Answer

Call the 3rd side is c, the other sides are a and b.

We have $$c^2 = a^2+ b^2 -2ab \cos \theta =2^2+5^2-2.2.5.\cos \theta =29-20\cos \theta$$

$$-1 < \cos \theta < 1 \rightarrow 9 < c^2 < 49 \rightarrow 3 < c < 7$$

For your answer, there are 1 option of third side value: 6

Note: $$cos \theta \neq 1$$ because it will be not a triangle

kc_kennylau · Answer

@linh412986 just triangle inequality is enough :)

kc_kennylau · Answer

@linh412986 sorry for wasting your effort :/

anonymous · Answer

@kc_kennylau No matter, I think if having time, it is the best way to practice my basic skill of algebra