If `A D` is median of ` A B C` and `P` is a point on `A C` such that `a r\ ( A D P):\ a r\ ( A B D)=2:3,\ ` then `a r( P D C): a r\ ( A B C)` is `1:5` (b) `1:5` (c) `1:6` (d) `3:5`

Explanation

Given: `ar(ADP)`/`ar(ABD)`=`2/3`

Let the ar(ADP) be `2x` and ar(ABD) be `3x`

As, AD is the median and AD divides the triangle into two triangles of equal area.

`ar(ADC)=ar(ADP)+ar(PDC)`

`ar(PDC)=x`

`ar(ABC)=ar(ABD)+ar(ADC`

`3x+3x`=`6x`

ar(PDC):ar(ABC)=x:6x=1:6

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