Officer Aptitude Rating (OAR) Test 2025 – 400 Free Practice Questions to Pass the Exam

The chosen answer correctly represents the relationship of area ratios in the context of similar figures. When considering the areas of two similar shapes, the ratio of their areas (let's denote the areas as \(A_1\) and \(A_2\)) is proportional to the square of the ratio of their corresponding linear dimensions (denoted as \(d_1\) and \(d_2\)). Thus, the formula is expressed as:

\[

\frac{A_1}{A_2} = \left(\frac{d_1}{d_2}\right)^2.

\]

In this case, using the notation provided, the \(d^1/d^2\) term represents the ratio of the dimensions of the shapes, while \(a^1/a^2\) corresponds to the ratio of the areas. The squared term reflects the fundamental property of geometry that when the dimensions are scaled by a certain factor, the areas are scaled by the square of that factor. This principle is essential in various applications, especially in geometry and proportional reasoning, where understanding the relationship between linear measurements and area calculations is necessary.

In summary, the correctness of the selected formula stems from its accurate portrayal of the mathematical relationship between the ratios