The ratio of the lengths of two corresponding sides of two similar triangles is 15 : 14.
The ratio of the areas of these two triangles, in the order mentioned, is:

Correct option is C

Given:

The ratio of the lengths of two corresponding sides of two similar triangles = 15 : 14.

Formula Used:

The ratio of the areas of two similar triangles is the square of the ratio of the corresponding sides.
​$$\text{Ratio of areas} = \left( \frac{\text{Side 1}}{\text{Side 2}} \right)^2$$​​

Solution:

The ratio of the corresponding sides is given as 15 : 14.

The ratio of the areas =  $$\left( \frac{15}{14} \right)^2$$​​

​$$\left( \frac{15}{14} \right)^2 = \frac{15^2}{14^2} = \frac{225}{196}$$​​

The ratio of the areas of the two triangles is 225 : 196.