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# 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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