Question

What is the length of DC?

2 units
3 units
6 units
9 units

Answer 1

(B)DC=3 units

Explanation:

From the given figure, it can be seen that DE is parallel to BC, thus by using the basic proportionality theorem, we get

`(AE)/(EB)=(AD)/(DC)`

⇒
`(12)/(4)=(9)/(DC)`

⇒
`DC{*}12=9{*}4`

⇒
`DC{*}12=36`

⇒
`DC=(36)/(12)`

⇒
`DC=3`

Thus, the length of DC will be =3 units.

Answer 2

Answer : Second Option is correct.

Explanation :

Since we have given in the figure ,

AE=12 units

AD=9 units

EB=4 units

DC=x units

By using the BPT theorem, which states that

"If a line is drawn parallel to one side of a triangle in distinct point , the other sides are divided in the same ratio."

So, here we have a ΔABC,

in which DE║BC as shown in the figure ,

so, by using the BPT we get,

`(AE)/(EB)=(AD)/(DC)\\\\(9)/(x)=(12)/(4)\\\\(9)/(x)=3\\\\x=3`

Hence, length of DC = 3 units .