ΔABC and ΔDBC are on the same base BC but on opposite sides of it. AD and BC intersect each other at O. If AO = a cm, DO = b cm and the area of ΔABC = x cm2, then what is the area (in cm2) of ΔDBC?

Answer: Option C

Solution

Answer: Option C

Solution:

Area of ΔABC : Area of ΔBDC = a : b = ak : bk
$$\begin{array}{rl}& ak=x\\ & k=\frac{x}{a}\\ & bk=b\times \frac{x}{a}=\frac{bx}{a}\end{array}$$