Fiona's school is in the shape of a triangle, with three hallways connecting the corners. fiona enters the building and walks 90 yards through the first hallway to the first corner. then, she walks 60 yards through the second hallway to the second corner.
what are the possible lengths of the third hallway?
between 30 yards and 60 yards
between 30 yards and 90 yards
between 30 yards and 120 yards
between 30 yards and 150 yards

between 30 yards and 150 yards

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Let

x > the possible lengths of the third hallway in yards

Applying the Triangle Inequality Theorem

1) 90+60 > x

150 > x

Rewrite

x < 150 yd

2) 60+x> 90

x > 90-60

x > 30 yd

The possible lengths of the third hallway in yards is the interval

(30,150)

All real numbers greater than 30 yards and less than 150 yards

therefore

between 30 yards and 150 yards

the answer will be the last one