In ΔABC, DE II BC and AD/DB=4/5 . If DE = 12 cm, find the length of BC.

In ΔABC, DE II BC and AD/DB=4/5 . If DE = 12 cm, find the…

In ΔABC, DE II BC and $\frac{AD}{DB}=\frac{4}{5}$ . If DE = 12 cm, find the length of BC.

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 27 cm.

According to the given question,

In the above figure, ${AD \over AB} = {AE \over AC} = {DE \over BC}$ ...(i)

Given that, $\frac{AD}{DB}=\frac{4}{5}$

⇒ ${AD \over AB} = {4 \over 9}$

Now, putting this value in equation (i),

⇒ ${AD \over AB} = {DE \over BC}$

⇒ ${4 \over 9} = {12 \over BC}$

⇒ BC = 27 cm

Hence the value of BC is 27 cm.