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

Answer 2

Answer:

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

$2 < x < 18$

Step-by-step 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