Question

problem 8: (first taught in lesson 45) the lengths of two sides of a triangle are 9 and 19. find the lengths that the third side must be greater than and less than. after you enter your answer press go. greater than and less than

Explanation:

Step1: Apply triangle inequality theorem (difference of two sides)

Let the two sides be \(a = 9\) and \(b=19\). The difference of two sides of a triangle \(|b - a|\) gives the lower - bound. So, \(19−9\).

Step2: Apply triangle inequality theorem (sum of two sides)

The sum of two sides of a triangle \(a + b\) gives the upper - bound. So, \(19 + 9\).

Answer:

Greater than \(10\) and less than \(28\)