Q22 of 31 Page 232

AD is the median of triangle ABC and P is any point on side AC in such a way that area of triangle ADP : area of triangle ABD = 2 : 3. Let us write area of triangle PDC : area of triangle ABC.


Area of triangle ADP : area of triangle ABD = 2 : 3


As AD is median


area of triangle ADB = area of triangle ADC = × area of triangle ABC


Let triangle ADP be 2x


And triangle ABD be 3x


Then Area of triangle ABC = 2 × Area of triangle ABD


= 2 × 3x


= 6x


area of triangle ADB = area of triangle ADC


area of triangle ADB = area of triangle ADP + area of triangle PDC


3x = 2x + area of triangle PDC


Area of triangle PDC = x


area of triangle PDC : area of triangle ABC


x : 6x


1 : 6


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