Question

If AD is median of ΔABC and P is a point on AC such that
ar (ΔADP) : ar (ΔABD) = 2 : 3, then ar (Δ PDC) : ar (Δ ABC)

(a) 1 : 5

(b) 1 : 5

(c) 1 : 6

(d) 3 : 5

Answer 1

Given: (1) AD is the Median of ΔABC

(2) P is a point on AC such that ar (ΔADP) : ar (ΔABD) =

To find: ar (ΔPDC) : ar (ΔABC)

We know that” the medians of the triangle divides the triangle in two two triangles of equal area.”

Since AD is the median of ΔABC,

ar (ΔABD) = ar (ΔADC) ……(1)

Also it is given that

ar (ΔADP) : ar (ΔABD) = ……(2)

Now,

Therefore,

Hence the correct answer is option (c).