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In the figure, $AB = 12$, $FE = 8$, $BC = CD = DE = 3$, $AB\perp BE$, $FE\perp BE$,

Then find the area of $\Delta GCD$.

 

 Jan 23, 2021
 #1
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Call the altitude of triangle GCD , GH

 

And triangle  GHC    is similar to  triangle  FEC

Call  HC,  x

 

So  we have  that

FE/CE =  GH /  x

8/6  = GH /x

4/3 = GH /x

GH  = (4/3)x

 

And triangle  GHD  is similar to  triangle  ABD

So

AB/ BD  =  GH / HD

Let HD  = 3  - x

So

12/6 =  [ (4/3)x ]  /   ( 3 - x)

2 (3 - x)  = (4/3)x

6 - 2x  = (4/3)x

6   =  ( 4/3 + 2) x

6 =  ( 10/3) x

x = 18/10 =  9/5

So GH  =(4/3) (9/5)  =   36/15 =  12/5

 

So  the  area of   GCD   =  (1/2) CD * GH   =  (1/2) (3) ( 12/5)  =  18/5  units^2

 

 

cool cool cool

 Jan 23, 2021

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