COMEDK · Maths · 27. Application of Derivatives
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 \(x\). The maximum area enclosed by the park is
- A \(\dfrac{1}{2} x^2\)
- B \(\pi x^2\)
- C \(\dfrac{3}{2} x^2\)
- D \(\sqrt{\dfrac{x^3}{8}}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{1}{2} x^2\)
Step-by-step Solution
Detailed explanation
Let the two sides of the triangular park having fence be \(x\) and \(x\). Let the angle between these two sides be \(\theta\). The area \(A\) of the triangle is given by the formula \(A = \dfrac{1}{2} \times x \times x \times \sin(\theta) = \dfrac{1}{2} x^2 \sin(\theta)\). To…
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