Question

A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n? 5 < n < 15 5 < n < 20 15 < n < 20 15 < n < 25 How far would Pete walk if he went from A to B to C? yards The direct distance from A to C is more than yards. The inequality w < represents the distance, w, that Pete might save by taking the direct path.

Answer 1

answer is D
15 < n < 25
see picture

Explanation:

Answer 2

`15 < n < 25`

Explanation:

Given

`Side\ 1 = 20cm`

`Side\ 2 = 5cm`

`Side\ 3 = n`

Required

Determine n using inequality

The three sides of the triangle must satisfy two of the following conditions

`Side\ 1 + Side\ 2 > Side\ 3`

`Side\ 1 + Side\ 3 > Side\ 2`

`Side\ 2 + Side\ 3 > Side\ 1`

Substitute values in the above inequalities;

`20 + 5 > n`

`20 + n > 5`

`5 + n > 20`

Solve each of the inequalities

`20 + 5 > n`

`25 > n`

`n < 25`

`20 + n > 5`

`n > 5 - 20`

`n > -15`

`5 + n > 20`

`n > 20 -5`

`n>15`

Since, the second inequality has negative, we simply ignore it

So, we combine the first and the third:

`n>15` and
`n < 25`

`15 < n` and
`n < 25`

Combine both

`15 < n < 25`

The second question is not clear and it is unanswerable