Triangle geometry

Question

Two sides of a triangle have links of five and 18 which expression describes the length of the third side

Answer 1

If you take two sides of a triangle as 5 and 18 and move them closer and closer together like this:

Eventually they will get extremely close to touching, but they cannot line up on top of each other and still be a triangle. If they DID lie on top of one another the distance of the connecting segment would be 18 - 5 or 13 units long. But again, that won't be a triangle, it would just be three line segments sitting on top of one another. So the third side MUST be greater than 13.

The same holds true if you take the two sides and "open" them up like this:

Eventually, they will almost form a straight line but, again, they must always be less than a straight line otherwise they wouldn't form a triangle. If they WERE a straight line, that line would be 5 + 18 or 23 units long so the length of the third side MUST be less than 23.

So the length of the third side is > 13 and < 23