∆ABC ~ ∆EDF and area(ΔΑΒC):area(∆EDF) = 1 : 4. If AB = 7 cm, BC = 8 cm and CA = 9 cm, then DF is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 16 cm.
Using,concept of similarity,
Area of ∆ABC/Area of ∆EDF = (Correspondence side of ∆ABC/Correspondence side of ∆EDF)2
1/4 = (Correspondence side of ∆ABC/Correspondence side of ∆EDF)2
1/2 = (Correspondence side of ∆ABC/Correspondence side of ∆EDF)
1/2 = BC/DF
DF = 8 × 2 = 16 cm
Hence, the length of DF is 16 cm.