Discussion

Explanation:

Area of triangle AOB = 4, DOC = 9, AOD = x and BOC = y

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In a quadrilateral, product of area of diagonally opposite triangles is same.

∴ 4 × 9 = x × y
⇒ xy = 36

Area of quadrilateral = 4 + 9 + x + y
Now we need to minimise 4 + 9 + x + y
This is possible when x + y is least possible.

We know, AM ≥ GM
(x + y)2 ≥ xy
⇒ (x + y) ≥ 12
∴ Least possible value of x + y = 12

⇒ Least possible area of the quadrilateral = 4 + 9 + x + y = 25

Hence, option (b).

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