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JEE Main20245 Apr 2024Morning ShiftMathematicsApplication of DerivativesActual

Let a rectangle A B C D of sides 2 and 4 be inscribed in another rectangle P Q R S such that the vertices of the rectangle A B C D lie on the sides of the rectangle P Q R S . Let a and b be the sides of the rectangle P Q R S when its area is maximum. Then (a+b)^2 is equal to :

Options

  1. A72
  2. B60
  3. C64
  4. D80

Correct answer

A. 72

Step-by-step solution

aligned & Area =(4 +2 )(2 +4 ) & =8 ^2 +16 +4 +8 ^2 & =8+20 & =8+10 2 & Max Area =8+10=18( 2 =1) =45^ & (a+b)^2=(4 +2 +2 +4 )^2 & =(6 +6 )^2 & =36( + )^2 & =36( 2 )^2 aligned =72

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