Finding Area of the Triangle

Question

In the figure, the ratio of AD to DC is 3 to 2. If area of $\Delta ABC$ is 40 $cm ^ {2}$ , what is the area of $\Delta BDC $

Answer 1

Hint:
The area of a triangle is equal to the height times the base. Now the two triangles $\Delta ABD$ and $\Delta BDC$ have the same height, so their areas are proportional to their bases.

Hope this helps.

Answer 2

Assume D as origin and A and C on x axis. So cordinates of A $(-3h,0)$ and C $(2h,0)$ where $h$ can be any real number. Now BD line is a line passing through origin. SO write it's equation $y=kx$ and assume cordinates of B as $(p,kp)$. Now area of triangle ABC is $A_1=\frac{5kph}{2}$ and area of triangle BDC is $A_2=kph$

Now you can find $A_2$ as $A_1$ is given as $40$.

Hope this will help !