Question

finding possible side lengths of a triangle
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

Explanation:

Step1: Apply triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So we have three inequalities:

1. \(n + 5>20\), which simplifies to \(n>15\).
2. \(n + 20>5\) (this is always true for positive - valued \(n\)).
3. \(5 + 20>n\), which simplifies to \(n<25\).

Answer:

D. \(15 < n < 25\)