Question

the median of a triangle ABC interest each other at point G. if one of its median is AD then prove that (1) ar(triangle ABD) = 3 multiply by ar(BGD) (2) ar(triangle ACD) = 3multiply by ar(triangle CGD).

Answer 1

Answer:HOPES THIS HELPS U.

we know if the two triangle have same height and different base ,

then ratio of their area is equal to the ratio of their respective base .

since AD is a median

hence BD=CD

THEREFORE , area of triangle ABD= ACD ( both the triangle have same height and same base )

hence, area of ABD =1/2( AREA of ABC)———(1)

Also, area of ABP=1/3(Area of ABD)=1/3* 1/2(ABC)

HENCE Area of ABP=1/6( Area of ABC)