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KVPY2019MathematicsApplication of Derivatives

Among all the parallelograms whose diagonals are 10 and 4 , the one having maximum area has its perimeter lying in the interval

Options

  1. A( 19 , 20 ]
  2. B( 20 , 21 ]
  3. C( 21 , 22 ]
  4. D( 22 , 23 ]

Correct answer

C. ( 21 , 22 ]

Step-by-step solution

Area of parallelogram whose diagonals are 10 and 4 and if angle between adjacent side is θ is A = 10 × 4 sin θ The area will be maximum if θ = π 2 , so the parallelogram must be rhombus Perimeter of rhombus = 4 29 = 464 and 464 ∈ ( 21 , 22 ]

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