In triangle ABC, D is a point on BC such that BD : DC = 3 : 4. E is a point on AD such that AE : ED = 2 : 3. Find the ratio area (ΔECD) : area (ΔAEB).
Answer & explanation
Correct answer: option 2
\(\frac{Area\; of \; AEB}{Area\;of\;EBD}\) = \(\frac{2}{3}\) ...(1)
\(\frac{Area\; of \; EBD}{Area\;of\;ECD}\) = \(\frac{3}{4}\) ..(2)
From eq (1) and (2), we have
\(\Delta \)AEB : \(\Delta \)EBD : \(\Delta \)ECD
2 : 3 : 4
Now,
\(\frac{Area\; of \; ECD}{Area\;of\;AEB}\) = \(\frac{4}{2}\) = \(\frac{2}{1}\)= 2 : 1
Therefore, the required ratio is 2 : 1.