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:

$15 < n < 25$

Step-by-step 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