Answer:
1 and 9
Step-by-step explanation:
By the Triangle Inequality Theorem, the sum of two side lengths of a triangle is always greater than the length of the third side.
In other words, in a triangle with side lengths [tex]a, b,[/tex] and [tex]c,[/tex] we always have [tex]a+b > c.[/tex]
Applying this to this question, the other side length, [tex]x,[/tex] must satisfy the following inequalities:
[tex]4+5 > x,\\x+5 > 4,\\x+4 > 5.[/tex]
Solving these inequalities gives
[tex]x < 9,\\x > -1,\\x > 1.[/tex]
Combining these solutions, we have [tex]1 < x < 9.[/tex] Therefore, the length of the third side falls between 1 and 9.
