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P is the midpoint of ¯BD . AP=BP=4, ¯AP¯BD¯BD¯DC¯AB¯BC. In simplest radical form, what is the perimeter of pentagon ABCDP?

 Mar 16, 2021
 #1
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2BP=BD

 

2*4=8

 

BD=DC

 

BD^2 + DC^2 = BC^2

 

8^2 + 8^2 = 64 + 64 = 2*64= 128 = 82

 

BP^2 + AP^2 = AB^2

 

4^2 + 4^2 = 16 + 16= 2*16=32 = 42

 

4sqrt2 + 4 + 4 + 8 + 8sqrt2 = 16 + 12sqrt2

 Mar 16, 2021
 #2
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Thanks for explaining, your answer is right :)

alliegoseo5  Mar 17, 2021

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