If AD is a median of triangle ABC and P is a point on AC such that ar(ADP): ar(ABD) = 2:3, then ar(PDC) : ar (ABC) is??

Asked by kumar.ashlesha | 12th Dec, 2014, 08:37: PM

Expert Answer:

fraction numerator A r. space A D P over denominator A r. space A B D end fraction equals 2 over 3 A r. space A D P space equals space 2 x comma space A r. space A B D space equals 3 x A r. space A B D space equals A r. space A D C space equals 3 x left square bracket S I n c e space A D space i s space t h e space m e d i a n space a n d space A D space d i v i d e s space t h e space t r i a n g l e space i n t o space t w o space t r i a n g l e s space o f space e q u a l space a r e a s right square bracket A r. space A D C space equals A r. space A D P plus A r. space P D C rightwards double arrow 3 x equals 2 x plus A r. space P D C rightwards double arrow A r. space P D C equals x A r. space A B C space equals space A r. space A B D plus A r. space A D C equals 3 x plus 3 x equals 6 x fraction numerator A r. P D C over denominator A r. space A B C end fraction equals fraction numerator x over denominator 6 x end fraction equals 1 over 6

Answered by Prasenjit Paul | 13th Dec, 2014, 09:57: AM