Question

If $\mathrm{PQ}$ and $\mathrm{PR}$ are the two sides of a triangle, then the angle between them which gives the maximum area of the triangle is

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

Answer 1

The correct option is D

$\frac{\pi }{2}$

Explanation for Correct option :

Assume $\mathrm{PQ}=\mathrm{a}$ and $\mathrm{PR}=\mathrm{b}$.

$\therefore \Delta =\left(\frac{1}{2}\right)ab\sin \theta \because (-1\le \sin \theta \le 1)$

Since the area is maximum when $\mathrm{sin\theta }=1$

$\therefore \theta =\frac{\pi }{2}$

Hence, Option (D) is Correct.