Verified Solution • 2025–26 Session moderate

QJEEM06Ma84a3: JEE Main 2006 Mathematics - Class 12 JEEM06Ma84a3 Solution: A triangular park is enclosed on two sides by a fence and on…

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length xx . The maximum area enclosed by the park is

Multiple Choice Options

  • A 32x2{3 \over 2}{x^2}
  • B x38\sqrt {{{{x^3}} \over 8}}
  • C 12x2{1 \over 2}{x^2}
  • D πx2\pi {x^2}

Step-by-Step Verified Solution

Area =12x2 sin⁡ θ= {1 \over 2}{x^2}\,\sin \,\theta

AIEEE 2006 Mathematics - Application of Derivatives Question 198 English Explanation

Maximum value of sin⁡θ\sin \theta is 11 at θ=π2\theta = {\pi \over 2}

Amax⁡=12x2{A_{\max }} = {1 \over 2}{x^2}

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