A triangular park is enclosed on two sides by a fence and on the...

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

Options

A $\frac{3}{2} x^2$
B $\sqrt{\frac{x^3}{8}}$
C $\frac{1}{2} x^2$
D $\pi \mathrm{x}^2$

Correct answer

C. $\frac{1}{2} x^2$

Step-by-step solution

Area

=\frac{1}{2} x^2 \sin \theta

A_{\max }=\frac{1}{2} x^2\left(\right.

at \left.\sin \theta=1, \quad \theta=\frac{\pi}{2}\right)

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