A triangle has two sides that measure 6 and 8. Write an inequality that shows a range for the length of the third side, x. Explain.
First, we will need to review the rule for the third side of a triangle.
The rule states: " the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides"
So we will assume that the third side is x.
We are given the other sides are 6 and 8
The first part is that "x" should be less than the sum of the other two sides.
==> x < 6+8
==> x < 14............(1)
The second part states that "x" should be greater than the difference between the other two sides.
==> x > 8-6
==> x > 2............(2)
Now combining (1) and (2) we get the following inequality.
==> 2 < x < 14
Then, the third side should measure between 2 and 14.