The areas of two similar triangles are respectively 16 m² and 36 m². Find the ratio of their corresponding sides.

Correct option is C

Given:

The areas of two similar triangles are respectively 16 $$m^2$$ and 36 $$m^2$$

Concept Used:

The areas of two similar triangles are proportional to the square of the ratio of their corresponding sides.

​$$\frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \left( \frac{\text{Side of Triangle 1}}{\text{Side of Triangle 2}} \right)^2$$​​

Solution:

We know that the areas of the triangles are 16 m² and 36 m². Therefore, the ratio of their areas is:

​$$\frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \frac{16}{36}$$

​​Let the ratio of the corresponding sides be rrx and y  So,

​$$\frac{16}{36} = \frac{x^2}{y^2}$$ 

​$$\frac{x}{y} =\sqrt \frac{16}{36} = \frac{4}{6}$$ 

Thus, the ratio of the corresponding sides of the two triangles is 4:6. 

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