Question

In the given figure, the ratio AD to DC is 3 to 2. If the area of Δ ABC is 40 cm², what is the area of Δ BDC?

Answer 1

Area of triangle ABC is given 40 cm².

Also `AD : DC = 3:2`

We are asked to find the area of the triangle BDC

Let us take BE perpendicular to base AC in triangle ABC.

We assume AC equal to y and BE equal to x in triangle ABC

Area of triangle ABC, say A is given by

`A = 1/2 ` ( Base × Height)

`40 = 1/2 (AC xx BE )` 

`40 = 1/2 ( y xx x)`

`xy = 40 xx 2`

xy = 80

We are given the ratio between AD to DC equal to 3:2

So,

`AD = 3/5 y`

`DC = 2/5 y`

In triangle BDC, we take BE as the height of the triangle

Area of triangle BDC, say A₁ is given by

`A_1 = 1/2 `( Base × Height ) 

`A_1 = 1/2 ( DC xx BE ) `

`A_1 = 1/2 (2/5y xx x)`

`A_1 = 1/5 xy `

`A_1 = 1/5 xx 80 ( as xy = 80 ) `

`A_1 = 16   cm^2`