Math Puzzle: Go To Great Lengths

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A quadrate is divided into 8 rectangles of adjacent area. One of these rectangles has a width of 8. What are nan lengths of nan sides of nan square?

Graphic shows a ray yellowish quadrate divided into 8 rectangles that person varying dimensions but adjacent areas. One of nan rectangles is highlighted successful a darker yellowish and 1 of its shorter sides is branded pinch nan number eight.

If nan rectangle pinch width 8 has magnitude a, its area is A = 8a. Now nan dimensions of nan different rectangles tin beryllium wished successively. We person B = C = a/2 × 16, D = a/3 × 24, E = 4a/3 × 6, F = 4a/15 × 30, G = 8a/5 × 5, and H = 8a/35 × 35. The quadrate truthful has a broadside magnitude of 35.

The aforesaid fig supra is shown pinch labels added for nan area (capital A) and longer broadside (lowercase italic a) of nan darker yellowish rectangle. The different 7 rectangles are branded pinch superior letters B, C, D, E, F, G and H.

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This puzzle primitively appeared successful Spektrum der Wissenschaft and was reproduced pinch permission. It was translated from nan original German type pinch nan assistance of artificial intelligence and reviewed by our editors.

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