Question

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

Answer 1

The correct option is C $\frac{1}{2}{x}^2$

Area $=\frac{1}{2}{x}^2\sin \theta$
$A_{max}$ at $\theta =\pi /2$
$\because$ $\sin \theta$ is max at $\theta =\pi /2$
$\therefore$ $A_{max}=\frac{1}{2}{x}^2$