Question

The angle between diagonals of a rectangle with perimeter 2p and area $\frac{3p^{2}}{16}$ is-

• A. tan^–1$\frac{1}{3}$
• B. tan^–1 $\frac{3}{4}$
• C. tan^–1 3
• D. None

Answer 1

Answer: (B)

tan^–1 $\frac{3}{4}$

Answer 2

Let dimension of rectangle are x, y

\ x + y = p

xy = $\frac{3p^{2}}{16}$

Solving x = $\frac{p}{4}$, y = $\frac{3p}{4}$

\ tan q = $\frac{1}{3}$

So required angle 2q = tan^–1 $\left( \frac{2.\frac{1}{3}}{1 - \frac{1}{9}} \right)$ = tan^–1$\frac{3}{4}$