Question

A gecko is in a room that is 12 feet long, 10 feet wide and 8 feet tall. The gecko is currently on a side wall ($10^{\prime}$ by $8^{\prime}$), one foot from the ceiling and one foot from the back wall ($12^{\prime}$ by $8^{\prime}$). The gecko spots a fly on the opposite side wall, one foot from the floor and one foot from the front wall. What is the length of the shortest path the gecko can take to reach the fly assuming that it does not jump and can only walk across the ceiling and the walls?

Answer 1

The shortest path the gecko can take is 20 feet long, consisting of 8 feet along the ceiling and 12 feet along the opposite side wall.

Step-by-step explanation:

Distances:

Gecko to ceiling edge: 1 foot

Ceiling edge to opposite wall edge: 10 feet (room width)

Opposite wall edge to fly: 1 foot

Path calculation:

Ceiling path: 1 foot (to edge) + 8 feet (along edge) = 9 feet

Side wall path: 1 foot (to edge) + 11 feet (remaining wall) = 12 feet

Shortest path:

Add ceiling and wall paths: 9 feet + 12 feet = 20 feet

Therefore, the shortest path for the gecko is 20 feet long.

Answer 2

Answer: The shortest is 22.4 feet

Step-by-step explanation: For the gecko to walk the shortest distance, it has to go straight from where it is to the celling, diagonally from the celling to the wall where the fly is and straight from the corner of the celling to where the fly is.

straight from where it is to the celling: 1 feet

diagonally from the celling to the wall where the fly:

it is a right triangle hipotenuse what we want, leg 12 and 8. (see picture attached): h² = 12² + 8² h = √208 h = 14.4 feet

straight from the corner of the celling to where the fly is: 7 feet.

1 + 14.4 + 7 = 22.4