JEE Main 2024 Mathematics question
Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle PQRS. Let a and b be the sides of the rectangle PQRS when its area is maximum. Then (a + b)² is equal to:
Answer: (A)
Solution
With the inner rectangle inclined at θ, a = 4 cos θ + 2 sin θ and b = 4 sin θ + 2 cos θ, so the area ab =
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