A ladder 5 metres long leans against a wall. A box measuring 1x1x1 meters just fits in the gap.
If the base of the ladder is nearer to the wall than the top of the ladder is to the ground, how far is the base of the ladder from the wall?
If a is the distance of the base of the ladder from the wall and b is the height the ladder reaches on the wall, then
a^2 + b^2 = 25
a/b = 1/(b-1)
Wolfram Alpha solves these, giving (within the context of the puzzle):
a = 1/2 + sqrt(13/2) - 1/2 sqrt(23 - 2 sqrt(26))
b = -25 + 24 (1/2 + sqrt(13/2) - 1/2 sqrt(23 - 2 sqrt(26))) + (1/2 + sqrt(13/2) - 1/2 sqrt(23 - 2 sqrt(26)))^2 - (1/2 + sqrt(13/2) - 1/2 sqrt(23 - 2 sqrt(26)))^3
which W Alpha can then simplify to
1/2 + sqrt(13/2) + 1/2 * sqrt(23 - 2 * sqrt(26))
if you explicitly ask it to.
In approximate form, they are
a = 1.2605183529032357543 ... meters
b = 4.83850116068954908 ... meters
Edited on December 19, 2023, 9:34 am
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Posted by Charlie
on 2023-12-19 09:30:55 |
solution