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

Answer 1

Answer: (B)

Given that $AB = AC = x$
We know that area of isosceles triangle is maximum, if it is right angled triangle.
$\therefore $ Maximum area of triangle $=\frac{1}{2} x^{2}$