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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

A B C D and P Q R S are two variable rectangles such that P, Q, R and S lie on A B, B C, C D and D A respectively and perimeter ' ' of PQRS is constant. If maximum area of ABCD is 32 , then is equal to

Correct answer

4

Step-by-step solution

Here 2 a +2 ~b = i.e. a + b = 2 Area (A) of rectangle A B C D=A B B C aligned & =(A P+P B)(B Q+Q C)=(b +a )(a & +b ) aligned =a b+ (a^2+b^2 ) 2 2 aligned & A ab + a ^2+ b ^2 2 or A _ = ( a + b )^2 2 =32 & ^2 8 =32 or =16 aligned

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