Brainteaser

The measurements of a room are 18' x 8' x 16' (L x W x H). A gecko is on wall CDHG at 2 feet above the midpoint of CG. Its food, an insect, is on wall BAEF at 2 feet below the midpoint of AE. Assuming that the insect will not move from its current position, what is the shortest distance the gecko must travel to reach its food? [Note: A gecko can’t fly.]

Solution below.


Solution to Brainteaser

If we mentally spread the walls of the room shown in the brainteaser, we will get six rectangles as shown (“g” is the gecko and “i” is the insect).

Now we can draw a right triangle.

We know that AB = 16, i is 2 feet from the top of the wall, and x is 2 feet from the bottom of the wall. Therefore, the length of ix must be 12.

We also know that FG = 18. The horizontal distance from x to the wall FE = 4. The horizontal distance from g to the wall HG = 4. Therefore, xg must equal 26.

Now we can apply the Pythagorean Theorem a2 + b2 = c2 where c is the hypotenuse of a right triangle. In this case let’s call it “d” for distance.

Therefore 122 + 262 = d2
144 + 676 = d2
d = 28.64 feet

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