The lengths of two sides of a triangle are 5 and 7 What is the range of possible side lengths

the sum of the two smaller sides of any real triangle must be > than the third side--otherwise the triangle is impossible!

7+12 means that the third side can be anything less than 19, at the most.

then  let's look at the other end of things: woujld 1, 7, 12 be a triangle? 

No because 1+7 would not be enough to build a triangle on a base of 12; that "1" would have to be >5.

I say that missing side x has to satisfy this: 5 < x < 19