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Analyzing the Pole-Corner Problem
Analyzing the Pole-Corner ProblemAnalyzing the Pole-Corner Problem
Analyzing the Pole-Corner Problem
A ten-foot-wide hallway meets a five-foot-wide hallway in the corner of a building. Find
the maximum length pole that can be moved around the corner without tilting the pole.
Maximum Length of Pole in Hallway
Maximum Length of Pole in HallwayMaximum Length of Pole in Hallway
Maximum Length of Pole in Hallway
The maximum length of a pole
c is the shortest line segment touching the interior corner
and opposite sides of the two hallways as shown in the diagram below.
Use proportional sides and the Pythagorean theorem to find the length
c with respect to
w. Then find the zeros of the first derivative of c(w). The minimum value of c(w) is the
maximum length of the pole.
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