In the given figure,the ratio of ADto DCis 3 to 2.If the area of triangle ABC is 40 cm²what is the area of triangle BDC?

Question

In the given figure,the ratio of ADto DCis 3 to 2 If the area of
triangle ABC is 40 cm2 what is the area of triangle
BDC?

Ankush Jain · Accepted Answer

Given, area of triangle ABC = 40 cm2 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 $= \frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times A D \times h e i g h t$ Similarly, area of triangle BDC $= \frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times D C \times h e i g h t$ Therefore, $\frac{a r e a o f t r i a n g l e A B D}{a r e a o f t r i a n g l e B D C} = \frac{\frac{1}{2} \times A D \times h e i g h t}{\frac{1}{2} \times D C \times h e i g h t} = \frac{A D}{D C} = \frac{3}{2}$ Again, area of triangle ABC = 40 cm2 â‡’ area of triangle ABD + area of triangle BDC = 40 cm2 â‡’ 3x + 2x = 40 â‡’ 5x = 40 â‡’ x = 8 Hence, area of triangle ABD = 3x = 3(8) = 24 cm2 and area of triangle BDC = 2x = 2(8) = 16 cm2

In the given figure,the ratio of ADto DCis 3 to 2.If the area of triangle ABC is 40 cm2 what is the area of triangle BDC?

In the given figure,the ratio of ADto DCis 3 to 2.If the area of triangle ABC is 40 cm²what is the area of triangle BDC?