In △ABC, point P∈AC with AP:PC=1:3, point Q∈AB so that AQ:QB=3:4, Find the ratios A(PBQ) : A(PBC) and A(AQP) : A(ABC)

The ratio APBQ : APBC is 4:21, AAQP : AABC is 3:28

Step-by-step explanation:

Data provided in the question

AP : PC = 1 : 3

So let us assume AP = x and PC = 3x.

And, If AQ : QB = 3 : 4

So, let us assume AQ = 3y and QB = 4y.

Now we have to find the area of ΔAQP and ΔABC

Therefore

Now

Now after solving these two ratios we can find

Therefore

Hence, we applied the above equation so that we can get to know the ratios