Correct Answer: 6 : 11

Solution : Given,
The ratio of the area of two similar triangles = 36 : 121
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
⇒ $\frac{\text{(Area of triangle)}{_1}}{\text{(Area of triangle)}{_2}}=\frac{(\text{side}{_1})^2}{(\text{side}{_2})^2}$
⇒ $\frac{\text{side}{_1}}{\text{side}{_2}}=\sqrt{\frac{\text{(Area of triangle)}{_1}}{\text{(Area of triangle)}{_2}}}$
⇒ $\frac{\text{side}{_1}}{\text{side}{_2}}=\sqrt{\frac{36}{121}}$
⇒ $\frac{\text{side}{_1}}{\text{side}{_2}}=\frac{6}{11}$
$\therefore \text{side}_{1} :\text{side}_{2}=6:11$
Hence, the correct answer is 6 : 11.