The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Finding the Width of a Corridor

Date: 11/13/95 at 19:42:41
From: Anonymous
Subject: The differential, extremas

A steel girder 27 ft long is moved horizontally along a passageway
8 ft wide and into a corridor at right angles to the passageway.
How wide must the corridor be for the girder to go around the corner?
Neglect the horizontal width of the girder.

Date: 11/15/95 at 16:20:36
From: Doctor Ken
Subject: Re: The differential, extremas


As your subject line indicates, this is a problem that will use Calculus
and local min/max stuff.  Here's a hint on how you might set it up:

                     |              |
                     |              |
                     |            / |
                     |          /   |
                     |        /     |
                     |      /       |
                     |    /         |
                     |  /           |
_____________________|/             |  _
                    / 27 ft.        |  |
                  /                 |  |
                /                   | 8 ft.
              /                     |  |
            /                       |  |
__________/_________________________|  -
                     |---- x ft. ---|

So you want to find the minimum value of x such that the girder can 
still go around the corner, right?  Well, for any value of x, there will 
be a "sticking point" where the girder will fit most tightly, i.e. where 
the girder's ends are closest to the walls of the corridors as the 
girder travels around the bend.  So we want to find the value of x where 
this sticking point makes both ends of the ladder exactly touch the 
walls.  See if you can find some similar triangles to help you out.

From here I'll direct you to a sketch I made using "The Geometer's 
Sketchpad."  If you have access to a Macintosh, you can look at the 
sketch by downloading a demo of the program from the URL   , and then you can download 
the sketch I made by using the URL   


-Doctor Ken,  The Geometry Forum

Associated Topics:
High School Calculus

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.