Geometry Ladder Problem

Date: 12/9/95 at 16:32:6
From: Anonymous
Subject: Geometry, triangles and equations

A figure shows a 12-foot ladder leaning across a 5-foot fence and 
touching a higher wall located 3 ft. behind the fence.  You want to find 
the distance x from the base of the ladder to the bottom of the fence.  
Let y equal the portion of the highest wall which starts at five 
feet and goes to the point where the ladder is touching it.  Using 
geometry, write two equations that show the relationship between x and 
y.  Justify what you wrote.

Date: 1/18/96 at 10:53:48
From: Doctor Ethan
Subject: Re: Geometry, triangles and equations

Hello,

    Well in my opinion, the most important thing to do in a problem like 
this is to draw a picture.  So let's do that.

                          _
                    /##    |
                   / ##    |y
                  /  ##    |
                 /   ##   _|
                /$   ##
               / $   ##
              /  $   ##

             |-x-| 

Here the $ is the fence, the ## is the wall, and the / is the ladder.

So, here is how I would approach it.

We need to think about similar triangles.  In particular find a triangle 
that has x as a side and one that has y as a side.  Are they similar?

If they are, then the sides are proportional. Now think about what kind of 
proportion you can set up.

Hope that this helps.

-Doctor Ethan,  The Math Forum