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?

A. $$\frac{a}{b}x$$

B. $$\frac{{ab}}{2}x$$

C. $$\frac{{bx}}{a}$$

D. $$\frac{{\left( {a + b} \right)}}{2}x$$

Answer: Option C

Solution (By Examveda Team)

Area of ΔABC : Area of ΔBDC = a : b = ak : bk
$$\eqalign{ & ak = x \cr & k = \frac{x}{a} \cr & bk = b \times \frac{x}{a} = \frac{{bx}}{a} \cr} $$