Question

If two sides of a triangle are given, then the area of the triangle will be maximum, if the angle between the given sides is

• A. $\frac{\pi}{3}$
• B. $\frac{\pi}{4}$
• C. $\frac{\pi}{6}$
• D. $\frac{\pi}{2}$

Answer 1

Answer: (D)

Let $a$ and $b$ be given, then area, $A=\frac{1}{2} a b \sin C$
$\Rightarrow \, \frac{d A}{d C}=\frac{1}{2} a b \cos C$

Hence, $A$ is maximum, when $\frac{d A}{d C}=0$
$\Rightarrow \, C=90^{\circ}=\frac{\pi}{2}$