+0  
 
0
66
3
avatar+71 

idk lol

 Jun 29, 2021
 #1
avatar+114012 
+3

I drew it.

Obviously, that is not exact but I believe it is close enough to answer the question.

Of course you are not meant to do it this way.  I was just having some fun.

Perhaps you can use my pic to help you with the exact geometrical calculations.  wink

 

Keep in mind that  180-135 = 45

 

 Jun 30, 2021
edited by Melody  Jun 30, 2021
edited by Melody  Jun 30, 2021
 #2
avatar+71 
+2

ok, thanks!

 Jun 30, 2021
 #3
avatar+120966 
+2

Using coordinate  geometry

Let A  = (0,0)

B =   (7,0)

C = (7  +  4cos 45  , 0  + 4sin 45)  =  ( 7  + 2sqrt 2 ,  2sqrt 2) 

D =  (7 + 2sqrt 2  ,  2 + 2sqrt 2)

E  = (7 + 2sqrt 2 -  (5/2)sqrt 2  ,  2  + 2sqrt 2 + (5/2)sqrt 2)  =  ( 7 - (1/2)sqrt 2 , 2 +(9/2)sqrt 2  )

F =   ( 7  -  (1/2)sqrt 2  - 6   ,  2  + (9/2) sqrt 2)   =   ( 1  - (1/2)sqrt 2 ,  2 + (9/2)sqrt 2 )

G =    ( 1  - (1/2)sqrt 2  - sqrt 2    ,  2  + (9/2)sqrt 2  -  sqrt 2)  =   (1 - (3/2)sqrt 2 ,2 + (7/2)sqrt 2  )

 

The  line   through   HA  has  the  equation    y =  -x

The line  through  GH   has  the  equation  x = 1 - (3/2)sqrt 2

So  the    coordinates of  H  =     ( 1 - (3/2) sqrt 2  , (3/2) sqrt (2)  -  1)

 

The  distance  from  A  to H  =    sqrt  ( 11  - 6sqrt 2)  =  3  -  sqrt 2     (simplified using WolframAlpha)

 

Distance  from   G to H   =  3  +  2sqrt 2

 

Total   perimeter   =    7 +  4  +   2  +   5   +  6  + 2   +   3 - sqrt 2  +  3  +  2sqrt 2  =  

 

32   +  sqrt 2

 

cool cool cool

 Jun 30, 2021

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