Question

What is the range of possible sizes for side x? it is a triangle with one side having 4.0, and the other having 5.6. picture attached below, thanks in advance :)

Answer 1

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;

$x=4.0+5.6$

$x=9.6$

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;

$x=5.6-4.0$

$x=1.6$

Thus, the range of possible values for x are $1.6$