SSC CGL 7 Sep 2016 Paper

Let, AB = BC = CA
= 2x units
∴ BD = BE = x units
Area of Δ ABC

= $\frac{\sqrt{3}}{4}\times {\left(2\mathit{x}\right)}^2$
= $\sqrt{3}{\mathit{x}}^2$ sq. units
Area of Δ BDE = $\frac{\sqrt{3}}{4}{\mathit{x}}^2$
∴ Area of a trapezium ADEC
= $\left(\sqrt{3}{\mathit{x}}^2-\frac{\sqrt{3}}{4}{\mathit{x}}^2\right)$ sq. units
= $\frac{3\sqrt{3}{\mathit{x}}^2}{4}$ sq. units
∴ Required ratio
= s $\sqrt{3{\mathit{x}}^2}$ : $\frac{3\sqrt{3}}{4}{\mathit{x}}^2$ = 4 : 3