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COMEDK202510 May 2025Evening ShiftMathematicsApplication of DerivativesActual

Quadrilateral PQRS is inscribed inside a rectangle of dimensions 10 ~cm 8 ~cm . The value of ' x ', if the area of the quadrilateral is minimum is

Options

  1. A9 cm
  2. B4 cm
  3. C4.5 cm
  4. D6.5 cm

Correct answer

C. 4.5 cm

Step-by-step solution

Let the rectangle be ABCD with AB = CD = 10 cm and AD = BC = 8 cm. Let AQ = x , BR = x , CS = x , and DP = x . The points are located as follows: Q is on AB such that AQ = x , so QB = 10 - x . R is on BC such that BR = x , so RC = 8 - x . S is on CD such that CS = x , so DS = 10 - x . P is on AD such that DP = x , so AP = 8 - x . The area of the quadrilateral PQRS is the area of the rectangle ABCD minus the sum of the areas of the four right-angled triangles at the corners: APQ , BQR , CRS , and DSP . Area of APQ =

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