Henry Ernest Dudeney/Modern Puzzles/132 - The Garden Bed/Solution
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Modern Puzzles by Henry Ernest Dudeney: $132$
- The Garden Bed
- A man has a triangular lawn of the proportions shown,
- and he wants to make the largest possible rectangular flower-bed without enclosing the tree.
Solution
From Largest Rectangle Contained in Triangle, the largest rectangle that can be inscribed within a triangle is situated such that:
This solution works only if the tree is sufficiently close to the corner that it is not enclosed inside at least one of those largest rectangles.
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $132$. -- The Garden Bed
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $262$. The Garden Bed