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

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. So, for sides \(a\), \(b\), and \(c\), we have \(|a - b| < c < a + b\).

Step2: Apply the theorem to the given sides

Here, the two given sides are \(20\) cm and \(5\) cm. First, find the difference of the two sides: \(20 - 5 = 15\). Then, find the sum of the two sides: \(20 + 5 = 25\). So, the third side \(n\) must satisfy \(15 < n < 25\) (since \(|20 - 5| < n < 20 + 5\)).

Answer:

\(15 < n < 25\) (the option with this inequality)