Question

Please solve q 91?

Answer 1

`|ABC|=30 " unit"^2`

Explanation:

Let `|ABC|` denote area of `DeltaABC`
Given `BD:CD=2:1, => |GBD|=2*|GDC|=2xx4=8`
let `|GDE|=a, => |CDE|=7-a`,
as `|EBD|:|EDC|=2:1, => (8+a):(7-a)=2:1, => a=2`
as `|GDB|:|GDE|=8:a=8:2=4:1`,
`=> BG:GE=4:1`
`=> |ABG|:|AGE|=4:1`,
let `|AGE|=b, => |ABG|=4b`
as `BD:DC=2:1, => |ABD|:|ADC|=2:1`
`=> (8+4b):(7+b)=2:1`
`=> 8+4b=2*(7+b)`
`=> b=3, 4b=12`
`=> |ABC|=8+4b+7+b=8+12+7+3=30 " units"^2`

Answer 2

Given

• `(BD)/(CD)=2/1`
• `DeltaGEC=3`
• `DeltaGCD=4`

The ratio of areas two triangles of same height is equal to the ratio of their bases.
So we can write

`(DeltaBGD)/(DeltaGCD)=(BC)/(CD)=(2CD)/(CD)=2`

`=>w/2=4=>w=8.....[1]`

For similar reason

`(x+y)/z=(BG)/(GE)=(w+4)/3=(8+4)/3=4`

`=>x+y-4Z=0.....[2]`

Similarly

`(x+y)/w=(z+3)/4`

`=>(x+y)/8=(z+3)/4`

`=>x+y-2z=6.....[3]`

By [2] and [3] we get `z=3`

So `x+y=12....[4]`

Again

`x/(w+4)=y/(z+3)`

`x/(8+4)=y/(3+3)`

`=>x/12=y/6`

`=>x=2y.....[5]`

By [4] and [5] we get `3y=12=>y=4`
and `x=2y=8`

So area of `Delta ABC=w+x+y+z+3+4`

`=>Delta ABC=8+8+4+3+3+4=30`sq unit