Question

Find the area of the rectangle $ABCD$ shown in the figure.

• A. $2500/\sqrt{2}$
• B. $2500$
• C. $2500/\sqrt{3}$
• D. $1250$
• E. $5000$

Answer 1

The correct option is C $2500/\sqrt{3}$

Let the point of intersection of the diagonals be $O$.

Let the midpoint of the side $BC$ be $P$.

$OP=25$

So the $\angle BOP$ = ${30}^{\circ }$

$tan\angle BOP=\frac{BP}{OP}$

$\Rightarrow$ $1/\sqrt{3}$ = $BP/25$

$\Rightarrow$ BP = $25/\sqrt{3}$

But as $ABCD$ is a rectangle $CD$ = $2$ $\times$ $BP$

$\therefore$ CD = $50/\sqrt{3}$

Area of the rectangle $ABCD=AB$$\times$ $CD=50$$\times$$50/\sqrt{3}$ = $2500/\sqrt{3}$