if x is an integer and 2<x<7, how many different triangles are there with sides of lenghts 2, 7 and x?

Question

posible answers only: 1,2,3,4 or 5

Answer 1

x is one of the numbers {3, 4, 5, 6}. On the surface that seems like 4 different triangles, but think about the sides and whether they *could* form valid triangles.

2, 7, 3 --> this doesn't work because the two smaller sides add to less than the largest side. That would never make a triangle... go ahead and try to draw it... 2 and 3 would never meet.
2, 7, 4 --> no good, same reason
2, 7, 5 --> no good, it's a straight line
2, 7, 6 --> This is the *only* valid triangle.

The answer is 1

The rule is that the two shorter sides must add up to *more* than the longest side.

Answer 2

If x can only represent whole numbers, then there are 4 possible triangles.

Answer 3

one

Answer 4

There are four.