The shortest distance between two points is a straight line, right? So one side of a triangle is a straight line. The path going along the other to sides isn't a straight line. So the side of a triangle is shorter than the sum of the other two sides.
So if a triangle has sides a, b, and c. c < a + b. a < b + c . And b < a + c. Always. (if they are proper triangles.)
Also if you have a triangle where one side is longer than the other, say c > b, then, as a + b > c, then a > c - b. Or in general c > |b - a|, b > |c -b| and a > |c - b|. This makes sense as is the distance of a third leg of a triangle has to be longer than simply going up one distant of one leg and straight back down the leg another.
Call the unknown side of the triangle x. So here you have three pieces of information:
Perimeter = 11.3 + 14.7 + x <= 44, Triangle Inequality: x < 11.3 + 14.7 ,Triangle Inequality variation: x > 14.7 - 11.3
The first one $\rightarrow$ 26 + x <= 44 $\rightarrow$ x <= 18.
The second one $\rightarrow$ x < 26. (This is weaker than the first one so we don't need it; if x <=18 then it's also x < 26).
The third one $\rightarrow$ x > 3.4 $\rightarrow$ 3.4 < x.
Combine to get 3.4 < x <= 18.
Any real number between 3.4 and 18 is an answer.