Question
Download Solution PDFD and E are points on the sides AB and AC, respectively, of ΔABC such that DE is parallel to BC and AD ∶ DB = 7 ∶ 9. If CD and BE intersect each other at F. then find the ratio of areas of ΔDEF and ΔCBF.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AD : DB = 7 : 9
DE ∥ BC
Calculation:
AD : DB = 7 : 9
So, AD : AB = 7 : (7 + 9) = 7 : 16
In ΔADE and ΔABC
∠ ADE = ∠ ABC --- (corresponding angle)
∠ AED = ∠ ACB --- (corresponding angle)
∠ A = ∠ A --- (common angle)
So, ΔADE ∼ ΔABC
AD : AB = DE : BC = 7 : 16
Now,
In ΔDEF and ΔBCF
∠ DEF = ∠ FBC ---(alternate angle)
∠ EDF = ∠ FCB ---(alternate angle)
∠ DFE = ∠ BFC --- (Opposite Angles)
So, In ΔDEF ∼ ΔBCF
Thus, areas of ΔDEF and ΔCBF
⇒ DE2 : BC2
⇒ 72 : 162
⇒ 49 : 256
∴ The correct option is 3
Last updated on Jul 21, 2025
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