Question

If sides of a triangle have lengths 8 ft and 12 ft.

Answer 1

`20 > c > 4`

Explanation:

Given

`Sides =8\ and\ 12`

Required

The third side

To do this, we make use of the triangle inequality theorem which implies that:

`a + b > c`

`a + c > b`

`b + c > a`

Where

`a,b,c\to sides`

So, we have:

`8 + 12 > c`

`8 + c > 12`

`12 + c > 8`

Solve all inequalities

`8 + 12 > c`

`20 > c`

`8 + c > 12`

`c > 4`

`12 + c > 8`

`c > -4`

Ignore negative inequalities.

So, we have:

`20 > c` and
`c > 4`

Combine

`20 > c > 4`

The above implies that the third length is between 5 and 19 (inclusive)