Question

Two sides of a triangle have lengths of 5x and 11x. The length of the third ide can be any number between ___ and ___.

Answer 1

You have to apply the triangle inequality!

Answer 2

I don't know how, though.
I'm trying to understand it, can you walk me through it?

Answer 3

It's a basic property of a triange: The sum of two side length must always be bigger then the third side length. It comes from the fact, that the sides of a triangle are the shortest connections between the points and if you take the connection going over the third point, you must get a longer path.
So if the side length are called a, b and c you get \[\begin{gather}a+b \geq c\\b+c \geq a\\c+a \geq b\end{gather}\]

Answer 4

Now just insert the given length and see which inequality gives you a range for the third side.