Question

the measures of two sides of a triangle are given. between what two numbers must the third side (s)fall? 10 and 15

Explanation:

Step1: Apply the triangle inequality theorem (sum of two sides)

Let the sides of the triangle be \(a = 10\), \(b=15\), and \(c\) be the third - side. According to the triangle inequality \(a + b>c\), so \(10 + 15>c\), which simplifies to \(c<25\).

Step2: Apply the triangle inequality theorem (difference of two sides)

Also, according to the triangle inequality \(|a - b|

Answer:

The third side \(s\) must fall between \(5\) and \(25\).