NTSE Stage 2 SAT 2018 Exam Question Paper

Let PQRS be the rectangular field with length l and width b and RT be the vertical pole.In ΔPRT
$\tan {30}^{\circ }=\frac{\mathit{R}\mathit{T}}{\mathit{P}\mathit{R}}$
$\frac{1}{\sqrt{3}}=\frac{10}{\mathit{P}\mathit{R}}$
$\mathit{P}\mathit{R}=\sqrt{{\mathit{l}}^2+{\mathit{b}}^2}=10\sqrt{3}$
${\mathit{I}}^2+{\mathit{b}}^2=100\times 3=300$.....(1)
In ΔSRT
$\tan {60}^{\circ }=\frac{10}{\mathit{S}\mathit{R}}\to \sqrt{3}=\frac{10}{\mathit{S}\mathit{R}}$
$\mathit{S}\mathit{R}=\frac{10}{\sqrt{3}}=\mathit{l}\to {\mathit{l}}^2=\frac{100}{3}$......(2)
Use equation (2) in (1),then
${\mathit{b}}^2=300-\frac{100}{3}=\frac{800}{3}$
Now,${\mathit{I}}^2{\mathit{b}}^2=\frac{100}{3}\times \frac{800}{3}=\frac{80000}{9}$
$\mathit{l}\mathit{b}=\sqrt{\frac{80000}{9}}=\frac{200\sqrt{2}}{3}$
Hence, the required area of rectangular field is $\frac{200\sqrt{2}}{3}$