Final answer:
The key geometry property of rectangles relevant to the student's question is that the area of a square is the square of the length of its side. This property can be used to compare areas of two squares by taking the ratio of the squares of their side lengths. Ratios and proportions involving lengths and widths are also fundamental to solving problems involving rectangles in various contexts.
Step-by-step explanation:
The student's question pertains to identifying and using a property of rectangles to solve a mathematical problem, possibly related to their areas. To answer the question, it is necessary to know that in mathematics, especially in geometry, rectangles have several defining properties. One key property is that opposite sides of a rectangle are parallel and equal in length. Additionally, the diagonals of a rectangle are equal in length and bisect each other.
When comparing the areas of two squares, as presumably being asked in the student's question, one can make use of the fact that the area of a square is the square of the length of one of its sides (Area = side²). To compare the areas, one would simply take the ratio of the squares of the lengths of the sides of the two squares.
In a scenario such as the one Beth describes, where proportions are used to define architectural elements, this concept also applies. The ratio of areas can reflect the proportional relationship between different parts of a structure.
Similarly, when assessing a physical situation such as pressure and area, as in the provided solutions, the area inside a rectangle can express a specific quantity such as work or energy, in terms of the product of height and width, which in the context of physics, could represent pressure and volume change respectively.
To write proportions by setting length ratios or width ratios equal to one another, you would take corresponding lengths from the rectangles in question and form an equation stating that the first length divided by the second length equals the third length divided by the fourth length. The same process applies to widths.