This puzzle is from the Irishman Owen O’Shea.
“The following puzzle illustrates a beautiful mathematical relationship involving a rectangle of any size and a random point within that rectangle that most people, including mathematicians, are unaware of.
The figure shows a rectangular room. There is a matchbox located 6 feet from one corner of the room and 27 feet from the opposite corner. The matchbox is also located 21 feet from a third corner.
How far is the matchbox from the fourth corner?”
See the Spot in a Rectangle Problem for a solution.
Another approach.
v^2 = 36 – x^2
y^2 = 729 – u^2
Adding,
v^2 + y^2 = 765 – ( x^2 + u^2)
Also X^2 + u^2 = 441
z^2 = v^2 + y^2 = 765 – 441 = 324
z = 18
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