Respuesta :

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,

[tex]\frac{AE}{EB}=\frac{AD}{DC}\\\\\frac{9}{x}=\frac{12}{4}\\\\\frac{9}{x}=3\\\\x=3[/tex]

Hence, length of DC = 3 units .

boffeemadrid

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

[tex]\frac{AE}{EB}=\frac{AD}{DC}[/tex]

⇒[tex]\frac{12}{4}=\frac{9}{DC}[/tex]

⇒[tex]DC{\times}12=9{\times}4[/tex]

⇒[tex]DC{\times}12=36[/tex]

⇒[tex]DC=\frac{36}{12}[/tex]

⇒[tex]DC=3[/tex]

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

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