If every side of a triangle is doubled, the area of the new triangle is K times the area of the old one. K is equal to :

Solution (By Examveda Team)

$$\eqalign{ & {{\text{A}}_{\text{1}}} = \frac{{\sqrt 3 }}{2}{a^2}{\text{ and }} \cr & {{\text{A}}_{\text{2}}} = \frac{{\sqrt 3 }}{2}{\left( {2a} \right)^2} \cr & \,\,\,\,\,\,\,\,\,\, = 4 \times \frac{{\sqrt 3 }}{2}{a^2} \cr & \,\,\,\,\,\,\,\,\,\, = 4{{\text{A}}_{\text{1}}} \cr & \therefore {\text{K}} = 4 \cr} $$