Final answer:
A square can be precisely defined as 'a rectangle with all sides of equal length' or 'a rhombus with all angles of 90 degrees.' Dimensional analysis using side lengths helps calculate area and perimeter of squares.
Step-by-step explanation:
Two student definitions that precisely define a square are:
- A. "A square is a rectangle with all sides of equal length." This definition specifies that a square has the properties of a rectangle (four right angles), with the added condition that all sides are of equal length.
- C. "A square is a rhombus with all angles of 90 degrees." This definition specifies that a square has the properties of a rhombus (all sides of equal length), with the added condition that all angles are right angles.
Option B is incomplete because not all parallelograms with opposite sides of equal length have four right angles. Option D is also correct, as it outlines the fundamental properties of a square, but within the context of this question, options A and C are the most precise definitions.
When it comes to dimensions, calculations for both perimeter and area are based on the length of a side. The perimeter of a square with side length a is 4a, and the area is a·a or a². Understanding the properties of shapes helps in calculating area and perimeter, especially in comparison problems like the one involving Marta's squares, where the larger square's sides are twice as long as the smaller ones. The area ratio of the larger to the smaller square is ² : 1 because the area increases by the square of the scale factor.