Finding Line Segment LengthsDate: 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 problems. 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 *---------*-----------*----------* |---------| 2x+32 |-----------| 10x+20 |---------------------| 112 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 *---------*-----------*----------* |----------| 6.5x-2 |-----------| x+20 |---------| 6.5x-2 |--------------------------------| 44 So it's a pretty similar problem. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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