The areas of two similar triangles are `36\ c m^2` and `100\ c m^2` . If the length of a side of the smaller triangle in 3 cm, find the length of the corresponding side of the larger triangle.

Explanation

To solve the problem step by step, we will use the properties of similar triangles and the relationship between their areas and corresponding sides.

### Step 1: Understand the relationship between the areas of similar triangles.
For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. This can be expressed as:
\[ \frac{\text{Area of triangle 1}}{\text{Area of triangle 2}} = \left(\frac{\text{Side of triangle 1}}{\text{Side of triangle 2}}\right)^2 \]

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