Question

fionas school is in the shape of a triangle, with three hallways connecting the corners. fiona enters the building and walks 60 yards through the first hallway to the first corner. then, she walks 80 yards through the second hallway to the second corner.
what are the possible lengths of the third hallway?
between 20 yards and 50 yards
between 20 yards and 150 yards
between 20 yards and 120 yards
between 20 yards and 250 yards

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Let \(a = 60\) and \(b=90\).

Step2: Calculate the lower - bound

\(|90 - 60|=30\).

Step3: Calculate the upper - bound

\(90 + 60 = 150\).

Answer:

between \(30\) yards and \(150\) yards