Question

plz guys answer it in detail
question no 12

Answer 1

Join AQ and CP.

Since CP is a median,

So Ar.(APC)= Ar.(ABC)/2

In triangle APC,

Since CR is a median,

Ar.(ARC)= 1/4 Ar.(ABC)-------(1)

Ar.(PRQ)= 1/2 Ar.(APQ)= 1/2 Ar.(BPQ)

Ar.(BPQ)= 1/4 Ar.(ABC)

or Ar. (PRQ)= 1/8 Ar.(ABC)

So. Ar.(PRQ)= 1/2 Ar.(ARC) [Since Ar.(ARC)= 1/4 Ar.(ABC)]

2). Ar.(RQC)=Ar.(RQB)

Ar.(ABC)= Ar.(RQB)+ Ar.(RQC)+ Ar.(ARC)

or Ar.(ABC)= 2 Ar.(RQC) + 1/4 Ar.(ABC) [Using (1)]

or 2 Ar.(RQC)= 3/4 Ar.(ABC)

or Ar. (RQC) = 3/8 Ar.(ABC)

Ar.(PBQ)= 1/4 Ar.(ABC)---------(2)

From (1) and (2)

3) Ar.(PBQ)= Ar.(ARC)