Geometry

Question Analysis
This question involves the concept of similarity in two - dimensional shapes and the relationship between the ratio of side lengths and the ratio of areas.
The main focus is on applying the principle that the ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

Key Concept Explanation
For two similar figures with a side - length ratio , the ratio of their areas and is given by .
This is because area is a two - dimensional measurement, and when the linear dimensions (side lengths) are scaled, the area scales by the square of the scale factor.

Step - by - Step Solution
Let the side - length ratio of the two squares be and , and let square centimeters be the area of the smaller square and be the area of the larger square.
We know that

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