Activities 89
3
Activities
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
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.
1. Define the expression for side
a in terms of
w and store it in a(w).
Note: When you want to define a function,
use multiple character names as you build
the definition.
2. Define the expression for side
b in terms of
w and store it in b(w).
10
5
w
a
b
c
a = w+5
b = 10a
w
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