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
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.