Question

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. A triangle is shown. The side lengths are 60 yards, 90 yards, and question mark. The top point is labeled exit and the bottom right point is labeled entrance. The distance between exit and entrance is question mark. What are the possible lengths of the third hallway?

Answer 1

Answer: between 30 and 150 yards.

Step-by-step explanation: edge 2023

Answer 2

Options

• between 30 yards and 60 yards
• between 30 yards and 90 yards
• between 30 yards and 120 yards
• between 30 yards and 150 yards

Answer:

(D)between 30 yards and 150 yards

Explanation:

The given hallways are 90 yards and 60 yards respectively.

By the triangle inequality: If a, b and c are the sides of a triangle, the sum of two sides (a and b) is greater than the third side c.

`60+x>90\\x>90-60\\x>30\\$Also, if the third unknown side is the longest side, we have:$\\90+60>x\\150>x\\x<150\\$Combining $x>30$ and $x<150$, we obtain: $ 30<x<150`

The possible values of the third side are real numbers between 30 yards and 150 yards.