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What is the length of DC?

2 units
3 units
6 units
9 units

What is the length of DC? 2 units 3 units 6 units 9 units-example-1
User Sbeam
by
9.0k points

2 Answers

3 votes

Answer:

(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.

User Chemikadze
by
7.7k points
1 vote

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 .

User Ghodss
by
7.5k points

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