Question

Determine the range of possible side lengths of the third side AB of triangle ABC from greatest to least

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

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

2 < x < 18