Question

in triangle ABC side AB,BC,and AC are produced upto points R,P,F respectively such that AB=BR,BC=CP and CA=AF prove that A(triangle PFR) =7A(triangle ABC)​

Answer 1

Answer:

Given that Sides AB,BC and CA of △ABC are produced up to points R,P,F respectively such that AB=BR,BC=CP, and CA=AF

Construction: Join PA,FB and RC

Let Area(△ABC)=a

We know that median of a triangle divides it into triangles of equal area.

In △PAB,AC is the median

⇒Area(△ABC)=Area(△APC)=a

In △PCF,PA is the median

⇒Area(△APC)=Area(△PFA)=a

In △BCF,BA is the median

⇒Area(△ABC)=Area(△ABF)=a

In △RAF,FB is the median

⇒Area(△ABF)=Area(△RBF)=a

In △ACR,BC is the median

⇒Area(△ABC)=Area(△RBC)=a

In △PRB,RC is the median

⇒Area(△RBC)=Area(△RPC)=a

Thus,Area(△ABC)=Area(△APC)=Area(△PFA)=Area(△ABF)=Area(△RBF)=Area(△RBC)=Area(△RPC)

Hence Area(△PRF)=a+a+a+a+a+a+a=7a=7(Area△ABC)

Step-by-step explanation:

hope its help full :)