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Just a question I don't understand, anything will help.

 

Given a triangle DEF with a segment GH parallel to EF. Find the length of FG given the following information. DG=x-4, FG=2x, DH=x-7, HE=x+3. Point H is located somewhere on line segment ED.

GobroSir  Feb 14, 2018
 #1
avatar+92395 
+2

Here's  a rough pic of the situation

 

                     

                                          D

                           x - 7                    x - 4        

 

                           H______________G

 

                    x + 3                                   2x

 

          E  ______________________________F

 

 

 

A segment parallel to a base of a triangle splits the sides in equal proportions

So

 

DH / HE  =  DG / GF      so we have

 

[ x - 7 ] / [ x + 3 ]  = [ x - 4 ] / [ 2x  ]   cross-multiply

 

 

2x (x - 7)  =  (x + 3) ( x - 4)   simplify

 

2x^2  - 14x    =  x^2  - x  - 12       rearrange as

 

x^2 - 13x  + 12  =  0

 

Factor   as

 

(x - 12) ( x - 1)  = 0

Setting to 0  and solving for x produces  x  = 12   or x  = 1

Reject the second soution since it makes (x - 7)  and (x - 4)  negative lengths

 

So  x  = 12    ⇒   FG  =  2(12)  =  24

 

Check that this works    5 / 15   =  8 / 24      true  !!!

 

cool cool cool

CPhill  Feb 14, 2018
edited by CPhill  Feb 14, 2018

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