Question

two side of a triangle have lengths 6 and 16 which inequalities describe the values that possible lengths for the third side

Answer 1

`22 > x > 10`

`10 < x < 22`

Explanation:

Given

`Side\ 1 = 6`

`Side\ 2 = 16`

Required

Determine the inequality that represents the third side

Represent the third side with x.

For the triangle to be true, two of the following condition must be true.

`6 + 16 > x`

`6 + x > 16`

`16 + x > 6`

`6 + 16 > x`

`22>x` -- True

`6 + x > 16`

`x > 16 - 6`

`x > 10` -- True

`16 + x > 6`

`x > 6 - 16`

`x > -10` --- False; Because, x can't be negative.

So, we have:

`22>x` and
`x > 10`

This can be combined to give:

`22 > x > 10`

or

`10 < x < 22`