Question

In the figure above, the area of triangle ABC is 6, if BC = CD what is he area of triangle ACD? A. 6 B.8 C.9 D.10

Answer 1

Answer: A

Given that:

`A_(ABC)=6`

And the formula for finding the area of a triangle is

`A=(1)/(2)bh`

We can rewrite this as

`A_(ABC)=(1)/(2)(AB)(BC)`
`6=(1)/(2)(AB)(BC)`

*Solve for BC

`(6)/(AB)=((1)/(2)(AB)(BC))/(AB)`
`(6)/(AB)=(1)/(2)(BC)`
`2*\lbrack(6)/(AB)\rbrack=\lbrack(1)/(2)(BC)\rbrack*2`
`(12)/(AB)=BC`

Now, given that BC = CD,

`(12)/(AB)=BC=CD`

Given that BC and CD are equal, this would mean that:

`BD=BC+CD`
`BD=(12)/(AB)+(12)/(AB)`
`BD=(24)/(AB)`

To find the Area of ACD, we will subtract the Area of ABC from the Area of ABD

`A_(ACD)=A_(ABD)-A_(ABC)`

We can rewrite this as:

`A_(ACD)=(1)/(2)(AB)((24)/(AB))-6`

Evaluate

`A_(ACD)=(1)/(2)(24)-6`
`A_(ACD)=12-6`
`A_(ACD)=6`

Therefore, the Area of ACD is 6.