Question

What is the length of DC? 2 units 3 units 6 units 9 units

Answer 1

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,

$\frac{AE}{EB}=\frac{AD}{DC}\\\\\frac{9}{x}=\frac{12}{4}\\\\\frac{9}{x}=3\\\\x=3$

Hence, length of DC = 3 units .

Answer 2

Answer:

(B)DC=3 units

Step-by-step explanation:

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

$\frac{AE}{EB}=\frac{AD}{DC}$

⇒$\frac{12}{4}=\frac{9}{DC}$

⇒$DC{\times}12=9{\times}4$

⇒$DC{\times}12=36$

⇒$DC=\frac{36}{12}$

⇒$DC=3$

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