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Each side of triangle \(ABC\) is extended such that \(AB=BP, BC=CQ, CA=AR,\) as shown in the diagram above.

If the area of triangle \(ABC\) is 10, then what is the area of triangle \(PQR?\)

 Jan 16, 2021
 #1
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(1/2) AB * BC  sin ABC  +  (1/2) BC * AC sin ACB  + (1/2) AC* AB  sin CAB   = 30  = 3 times area of ABC =

 

(1/2)  ( AB * BC sin ABC   +  BC * AC sin ACB   +  AC * AB sin CAB)  =  30

 

sin AB * BC sin ABC  +  BC * AC  sinACB   + AC* AB sin CAB       = 60     

 

sin ABC   = sin PBQ       sin ACB  = sin RCQ    sin  CAB  = sinRAP

 

Pink area   = 

 

(1/2) AB ( BC + BC)sin ABC   +  (1/2) BC ( AC + AC)sin ACB  +  (1/2) AC (AB + AB) sin CAB    =

 

 AB * BC  sin ABC   +  BC * AC sin ACB   +  AC* AB  sin CAB  =   60

 

So   [ PQR ]   = 10   +  60   =    70

 

cool cool cool

 Jan 16, 2021

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