by Susan Bricket

Published Friday May 10 2024 (link)

A French farmer’s estate is shaped like a right-angled triangle ABC on top of a square BCDE. The triangle’s hypotenuse is AB, and its shortest side, AC, has length 1 kilometre. Nearing retirement, the farmer decides to sell off the square of land and, obeying the Napoleonic law of succession, divide the triangle into three equal plots, one for each of his two children and a third for him and his wife in retirement. His surveyor discovers, surprisingly, that his remaining triangle of land can be divided neatly into three right-angled triangles, all identical in shape and size (allowing for reflections / rotations).

How many hectares did the farmer sell? (1 hectare = area of 100m x 100m plot)