Let a rectangle A BC D of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle A BC D lie on the sides of the rectangle PQRS . Let a and b be the sides of the r

Question

Let a rectangle A BC D of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle A BC D 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 :

TestHub · Accepted Answer

​ Area = ( 4 cos θ + 2 sin θ ) ( 2 cos θ + 4 sin θ ) = 8 cos 2 θ + 16 sin θ cos θ + 4 sin θ cos θ + 8 sin 2 θ = 8 + 20 sin θ cos θ = 8 + 10 sin 2 θ Max Area = 8 + 10 = 18 ( sin 2 θ = 1 ) θ = 4 5 ∘ ( a + b ) 2 = ( 4 cos θ + 2 sin θ + 2 cos θ + 4 sin θ ) 2 = ( 6 cos θ + 6 sin θ ) 2 = 36 ( sin θ + cos θ ) 2 = 36 ( 2 ​ ) 2 ​ = 72

Mathematics - Application of Derivative Question with Solution | TestHub

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