Two poles, 7ft and 5ft, joined by crossed lines — how high do they cross?
Two poles stand upright in a yard, one 7 feet tall and the other 5 feet tall. A line runs from the top of each pole down to the base of the other, crossing in between. How high above the ground is the point where the two lines cross?
Reveal the answer
2 feet 11 inches above the ground — and that height never depends on how far apart the poles are, only on their two heights. In general, two poles of height A and B produce a crossing height of (A×B)/(A+B): here (7×5)/(7+5) = 35/12 feet, which is 2 ft 11 in. Henry Dudeney set it as puzzle No. 186 in Amusements in Mathematics (1917).
— Henry Ernest Dudeney, Amusements in Mathematics — 1917, Puzzle No. 186, 'The Clothes Line Puzzle'
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