In the given figure,the ratio of ADto DCis 3 to 2.If the area of triangle ABC is 40 cm^{2 }what is the area of triangle BDC?

**Given,** area of triangle ABC = 40 cm^{2} and AD **:** DC = 3 **:** 2

Now, both the triangles ABD and BDC are lies between the same parallel and same base.

So, height of both the triangles are same.

Now, area of triangle ABD

Similarly, area of triangle BDC

Therefore,

Again, area of triangle ABC = 40 cm^{2}

⇒ area of triangle ABD + area of triangle BDC = 40 cm^{2}

⇒ 3x + 2x = 40

⇒ 5x = 40

⇒ x = 8

Hence, area of triangle ABD = 3x = 3(8) = 24 cm^{2}

and area of triangle BDC = 2x = 2(8) = 16 cm^{2}

**
**