THE GARDEN PUZZLE.
(
Patchwork Puzzles)
Professor Rackbrain tells me that he was recently smoking a friendly
pipe under a tree in the garden of a country acquaintance. The garden
was enclosed by four straight walls, and his friend informed him that he
had measured these and found the lengths to be 80, 45, 100, and 63 yards
respectively. "Then," said the professor, "we can calculate the exact
area of the garden." "Impossible," his host replied, "because you can
get an infinite number of different shapes with those four sides." "But
you forget," Rackbrane said, with a twinkle in his eye, "that you told
me once you had planted this tree equidistant from all the four corners
of the garden." Can you work out the garden's area?
Answer:
Half the sum of the four sides is 144. From this deduct in turn the four
sides, and we get 64, 99, 44, and 81. Multiply these together, and we
have as the result the square of 4,752. Therefore the garden contained
4,752 square yards. Of course the tree being equidistant from the four
corners shows that the garden is a quadrilateral that may be inscribed
in a circle.
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