Math Puzzle: Go to great lengths

A square is divided into eight rectangles of equal area. One of these rectangles has a width of 8. What are the lengths of the sides of the square?

If the rectangle with width 8 has length a, its area is A = 8 a . Now the dimensions of the other rectangles can be determined successively. We have B = C = a /2 × 16, D = a /3 × 24, E = 4 a /3 × 6, F = 4 a /15 × 30, G = 8 a /5 × 5, and H = 8 a /35 × 35. The square therefore has a side length of 35.

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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission. It was translated from the original German version with the assistance of artificial intelligence and reviewed by our editors.