Question

A triangle has two sides length 10 to 14 wht value could the length of the third side be

Answer 1

`4 < c < 24`

Explanation:

Given

`a = 10`

`b = 14`

Required

The possible length of c

Using triangle inequality theorem, we have:

`a + b > c`

`a + c > b`

`b + c > a`

So, we have:

`a + b > c`

`10 + 14 > c`

`24 > c`

Also:

`a + c > b`

`14 + c > 10`

`c > 10 - 14`

`c > - 4`

Lastly;

`b + c > a`

`10 + c > 14`

`c > 14 - 10`

`c > 4`

Write out all inequalities without negative consideration

`24 > c`

`c > 4`

Rewrite as:

`c < 24`
`4 < c`

Writing both together, we have:

`4 < c < 24`

Hence, the third side can take its value from the range:
`4 < c < 24`