Question

What is the range for the possible side length AB of ABC?

Answer 1

The range is from
`18` to
`2` (greatest to least)

`2 < x < 18`

Explanation:

we know that

The triangle inequality theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x-----> the length of the third side AB of triangle ABC

Applying the triangle inequality theorem

case A)

`8+10 > x`

`18 > x`

Rewrite

`x < 18`

case B)

`8+x > 10`

`x > 10-8`

`x > 2`

The solution for the range of possible side lengths of the third side is the interval

`(2,18)`

so

`2 < x < 18`

All real numbers greater than
`2` and less than
`18`

The number
`2` and the number
`18` are not included in the solution

Answer 2

2 < AB < 18

Explanation: