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In triangle ABC, AB = AC = 25 and BC = 20. Points D, E and F are on sides AB, BC and AC respectively, such that DE and EF are parallel to AC  and AB respectively. What is the perimeter of parallelogram ADEF?

 

 Jun 24, 2021

Best Answer 

 #2
avatar+151 
+2

i mean $ \overset{-}{AD}=\overset{-}{FE} $

 

knowing all that we can say that $\overset{-}{DB}$ and $ \overset{-}{DE} $ form an isosceles triangle so yes logically we get $\overset{-}{AB}=\overset{-}{DE}+\overset{-}{FE}=25 $

 

for the other side we can say that $ \overset{-}{AF}  $ and $\overset{-}{DE}$ have the same measurement -- so does $\overset{-}{FE}$ and $\overset{-}{FC}$ -- thus we can say that $\overset{-}{AC} = \overset{-}{DE} +  \overset{-}{FE}  = 25$ 

 

so yes, since we have the two sides just add them together 

 

although may i know why i cannot edit the original answer?

 Jun 24, 2021
 #1
avatar+151 
+2


 

 

look at the image -- since $ \overset{-}{AD} = \overset{-}{AC}   $ then we can say that $  \overset{-}{AB}=\overset{-}{DE}+\overset{-}{FE}=25    $


its the exact same from the other point of view, so its P would be $  25+25  $, which is equal to 50

 Jun 24, 2021
edited by UsernameTooShort  Jun 24, 2021
edited by UsernameTooShort  Jun 24, 2021
 #2
avatar+151 
+2
Best Answer

i mean $ \overset{-}{AD}=\overset{-}{FE} $

 

knowing all that we can say that $\overset{-}{DB}$ and $ \overset{-}{DE} $ form an isosceles triangle so yes logically we get $\overset{-}{AB}=\overset{-}{DE}+\overset{-}{FE}=25 $

 

for the other side we can say that $ \overset{-}{AF}  $ and $\overset{-}{DE}$ have the same measurement -- so does $\overset{-}{FE}$ and $\overset{-}{FC}$ -- thus we can say that $\overset{-}{AC} = \overset{-}{DE} +  \overset{-}{FE}  = 25$ 

 

so yes, since we have the two sides just add them together 

 

although may i know why i cannot edit the original answer?

UsernameTooShort  Jun 24, 2021
 #3
avatar+121048 
+1

I don't know why.....but.....that's an excellent answer   !!!!

 

cool cool cool

CPhill  Jun 24, 2021

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