Q. 45.0( 1 Vote )

P and Q are the mid-points of and in ΔABC. If the area of ΔAPQ = 12√3, find the area of ΔABC.

Answer :


In ∆ABC, P and Q are mid-points of AB and AC respectively.



The correspondence ∆APQ∆ABC is a similarity by SSS theorem.


Now,


Areas of similar triangles are proportional to the squares of their corresponding sides.





ABC = 12√3 × 4


ABC = 48√3


The area of ∆ABC is 48√3.


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