In the middle of a park there is a small, circular fish pond. One day a fish is dropped into the water. From the edge of the pond he happily swims 8 meters directly north and reaches a wall. He then turns due west and swims another 6 meters before again reaching a wall.
What is the diameter of the pond?
Scroll down for the answer.
The Answer:
The 8 meter and 6 meter measurements describes a rectangle that just "fits" inside the circular pond. A line drawn from opposite corners of this rectangle forms a right triangle whose hypotenuse is equal to the diameter of the pond.
Following from the "Theorem of Thales" and the "Theorem of Pythagoras" one obtains:
82 + 62 = d2
64 + 36 = d2
100 = d2
10 = d
Thus the diameter of the pond is 10 meters.
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