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Finding Line Segment Lengths

Date: 12/21/2001 at 18:49:50
From: Annie
Subject: Finding the length of segments

Can you help me find line segments AB and BC if points A,B,C, and D 
are collinear with B between A and C and C between B and D? 

The problems are: 

   1. AB = 2x + 32, BC = 10x + 20, AC = 112
   2. CD = 6.5x-2, BC = x+20, AB = CD, AD = 44

I would really appreciate it if you could help me with these two 

Thank you very much.

Date: 12/25/2001 at 12:23:10
From: Doctor Ian
Subject: Re: Finding the length of segments

Hi Annie,

I would never try to solve a problem like this without drawing a 
picture first, to help me keep track of the information that the 
problem gives me. 

We know that the points are collinear, and in the order ABCD:

   A         B           C          D

We're also given some of the segment lengths:

   A         B           C          D

Now, what's obvious from the picture, but not from the problem 
description, is that if you add AB and BC together, you have to end up 
with AC.  So

  (2x + 32) + (10x + 20) = 112

Can you take it from here?

Let's see what the picture tells us in the second problem:

   A         B           C          D

So it's a pretty similar problem. 

Does this help?

- Doctor Ian, The Math Forum   
Associated Topics:
High School Basic Algebra
High School Euclidean/Plane Geometry
High School Geometry
Middle School Algebra
Middle School Geometry
Middle School Two-Dimensional Geometry

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