Puzzle #46: Pi-thagoras
15 February 2020
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From New Scientist #3269, 15th February 2020 [link] [link]
Pythagoras’s theorem says that for any right-angled triangle, the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides.
There are some right-angled triangles whose sides are all whole number lengths. The simplest and best known is the “3-4-5” triangle (3² + 4² = 5²).
I have drawn a circle that fits precisely inside a 3-4-5 triangle. What is the area of the circle? Have a guess. And then see if you can prove that you are right.