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Given $dc = 7$, $cb = 8$, $ab = \frac{1}{4}ad$, and $ed = \frac{4}{5}ad$, find $fc$. Express your answer as a decimal.

 Jan 30, 2019
 #1
avatar+103948 
+1

We have that

 

AD = DC + CB + AB

AD =  7 + 8 + (1/4)AD

(3/4)AD = 15

AD = 15 * (4/3)  =  20

 

So  ED = (4/5)AD = (4/5)(20) = 16

 

Note that CA = CB + AB = 8 + (1/4)AD  = 8 + (1/4)16  = 8 + 4 = 12

 

So....by similar triangles

 

ED /AD  =  FC /CA

 

16 / 20 = FC / 12         

 

4 /5 = FC /12   multiply both sides by 12

 

12 * 4 /5  =  FC  =    48 / 5  =   9.6

 

 

cool cool cool

 Jan 30, 2019
 #2
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I dont think that is the right answer

Guest Jan 31, 2019
 #3
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Note that CA = CB + AB = 8 + 5  = 13[Cphill made a small typo here. CA should be 13 not 12.
So....by similar triangles
ED /AD  =  FC /CA
16 / 20 = FC / 13         
4 /5 = FC /13   multiply both sides by 13
13 * 4 /5  =  FC  =    52 / 5  =   10.4

 Jan 31, 2019
 #4
avatar+103948 
0

Thanks, Guest!!

 

 

cool cool cool

CPhill  Jan 31, 2019

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