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MHT CET20243 May 2024Morning ShiftMathematicsApplication of DerivativesActual

A triangular park is enclosed on two sides by a fence and on the third side a straight river bank. The two sides having fence are of same length x . The maximum area (in sq. units) enclosed by the park is

Options

  1. A3 2 x^2
  2. Bx^3 8
  3. C1 2 x^2
  4. Dx^2

Correct answer

C. 1 2 x^2

Step-by-step solution

Let ABC be on isosceles triangle such that AB = AC =x ABC = ACB = Draw seg AD side BC at point D . ABD is a right angled triangle such that AD =x and BD =x Similarly, in ACD , DC =x In A B C , aligned & Height = AD =x & Base = BC =x +x =2 x aligned aligned A ( ABC ) & = 1 2 x 2 x & = x^2 2 (2 ) & = x^2 2 2 aligned Since, -1 2 1 , for maximum value of 2 , Maximum area = x^2 2 sq. units.

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