Question
Download Solution PDFIn a ΔABC, DE ∥ BC, where D is a point on AB and E is a point on AC. If DE divides the area of ΔABC into two equal parts, then DB ∶ AB is equal to :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used
The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides & medians.
Calculation
As DE divides the area of ΔABC into two equal parts.
i.e. ar(ΔADE) = ar(DEBC)
⇒ ar(ΔADE) = ar(ΔABC)/2
⇒ ar(ΔABC)/ar(ΔADE) = 2
Now,
ΔABC ∼ ΔADE (By AAA similarity)
So,
ar(ΔABC)/ar(ΔADE) = (AB/AD)2
⇒ 2 = AB2/AD2
⇒ AB2/AD2 = 2
⇒ AB = √2AD
⇒ AB = √2(AB - DB)
⇒ √2AB - AB = √2DB
⇒ AB(√2 - 1) = √2DB
∴ DB/AB = (√2 - 1)/√2
The answer is (√2 - 1):√2
Last updated on Jul 22, 2025
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