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KVPY2017MathematicsApplication of Derivatives

In an isosceles trapezium, the length of one of the parallel sides, and the leng ths of the non-parallelsides are all equal to 30 . In order to maximize the area of the trapezium, the smallest angle should be

Options

  1. A6
  2. B4
  3. C3
  4. D2

Correct answer

C. 3

Step-by-step solution

In A B F, y=30 Area is A= 1 2 [60+60 ](30 ) array l =30(1+ )(30 ) =900( + ) array For maximum or minimum array l d A d =900 [ + (- ² + ² ) ]=0 -1+ ² + ² =0 2 ² + -1=0 (2 -1)( +1)=0 array = 1 2 or =-1 (not possible) =60^

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