The ratio of the lengths of two corresponding sides of two similar triangles is 9 : 1. The ratio of the areas of these two triangles, in the order mentioned, is:

Correct option is C

Given:

The ratio of the corresponding sides of two similar triangles is 9 : 1

Formula Used:

Ratio of Areas = $$\left(\frac{\text{Length of corresponding sides of the first triangle}}{\text{Length of corresponding sides of the second triangle}}\right)^2$$​

Solution:

Ratio of Areas = $$\left(\frac{9}{1}\right)^2 = \frac{9^2}{1^2} = 81: 1$$