Given:
Given that the two sides of the triangle are x, 4.0 and 5.6
We need to determine the range of possible sizes for the side x.
Range of x:
The range of x can be determined using the triangle inequality theorem.
The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".
Thus, applying the theorem, we have;
[tex]x=4.0+5.6[/tex]
[tex]x=9.6[/tex]
Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".
Thus, we have;
[tex]x=5.6-4.0[/tex]
[tex]x=1.6[/tex]
Thus, the range of possible values for x are [tex]1.6<x<9.6[/tex]
