Greetings Camryn from Madison,
Thank you for your question.
You asked if we are given the length of two sides of triangle, 7 and 13, what can we say about the third side.
There is a rule for every triangle known as the triangle inequality which states:
Triangle Inequality: The length of any side of any proper triangle is less than, the sum of the other two.
For a triangle with sides whose lengths are given as positive numbers a, b, c; this gives 3 inequalities:
a+b>c, b+c>a, c+a>b.
which can also be written as
Note: if you include degenerate triangles where all vertexes are on the same line (collinear,) then these inequalities can be equalities, but as degenerate triangles are not technically triangles, I didn't include them.
Back to your question, given a = 7 and b = 13, this gives us for c:
6 < c < 20,
Of course if you knew the triangle was a right triangle you could use the Pythagorean theorem to directly get the size of the third side.
Hope this helps.