### Scientist

# New Scientist puzzle #46: Pi-thagoras

12 February 2020 #46 Pi-thagoras 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…

12 February 2020

## #46 Pi-thagoras

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 (3^{2} + 4^{2} = 5^{2}).

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.

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