In the given figure, Δ ABC ~ Δ ADE. If AE: EC = 4: 7 and DE = 6.6 cm, find BC. If ‘x’ be the length of the perpendicular from A to DE, find the length of perpendicular from A to BC in terms of ‘x’.

Solution:

According to the given question,

   

So, we have

   

   

Or,

   

And, also

   

we have

   

And

   

So,

   

And,

   

   

In

   

   

[As DP || BQ, corresponding angles are equal.]

   

[As DP || BQ, corresponding angles are equal.]

So,

   

criterion for similarity

   

   

Hence,