Triangles

[naveenhv]

If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

a. None
b. I only
c. II only
d. II and III only
e. I, II and III

[RonPurewal]

a useful inequality that you should also know about triangles:

THIRD SIDE INEQUALITY
if you KNOW two sides of a triangle, then
DIFFERENCE < third side < SUM

this can be derived directly from the triangle inequality (the rule that says that the sum of the 2 shorter sides of a triangle must be longer than the longest side), but it's worth knowing separately; the last thing you want to do on a 2-minute problem is start deriving new rules.

in this problem, this rule immediately yields
5 - 2 < third side < 5 + 2
3 < third side < 7
... since the other two sides add up to 7, we have
10 < perimeter < 14
done.