Question

if AD is median of triangle ABC and P is a point on AC such that area of triangle ADP : area of triangle ABD = 2:3 then area of triangle PDC : area of triangle ABC is ​

Answer 1

Answer:

1:6

Step-by-step explanation:

Given, AD is a median of △ABC and P is a point on AC such that Area(△ADP):Area(△ABD)=2:3

⇒ Area(△ABD) = 2

Area(△ADP) 3

⇒Area(△ADP) = 2x and Area(△ABD) = 3x

Again AD being the median divides the △ABC in two triangles of equal area.

⇒Area(△ABD) = Area(△ADC) = 3x

Now, Area(△ADC) = Area(△ADP) + Area(△DPC)

or, 3x = 2x + Area(△PDC)

or, Area(△PDC) = x

Again, Area(△ABC) = Area(△ABD) + Area(△ADC) = 3x + 3x = 6x

Therefore, Area(△PDC):Area(△ABC) = x:6x = 1:6