First, the specific reasons:
When the perimeters of two rectangles are equal, their areas are not necessarily equal. It is possible that one of the rectangles has a large aspect ratio and the other has a small aspect ratio, so their areas are different. When the aspect ratio of two rectangles is equal, their areas are equal.
So when the perimeters of two rectangles are equal, their areas are not necessarily equal, and the equality of areas depends on the aspect ratio.
Second, the relevant formula:
1, area formula: rectangular area = length × width; s=a×b .
2. perimeter formula: rectangle perimeter = (length+width) × 2; c=(a+b)×2 .
The characteristics of rectangle and the definition of length and width;
First, the characteristics of the rectangle:
1, with equal sides:
The characteristic of a rectangle is that two groups of opposite sides are equal, that is, each corner is a right angle. This means that all four sides of a rectangle are equal and two adjacent sides are parallel to each other. This feature makes rectangle have advantages in symmetry and stability, so it is widely used in mathematics and engineering.
2, adjacent vertical:
The characteristic of a rectangle is that each corner is a right angle, the opposite sides are equal, the opposite sides are parallel and the adjacent sides are vertical. Adjacent sides perpendicular means that two adjacent sides are equal in length and perpendicular to each other. This property is of great significance in the study of cuboids, because the relationship between vertical edges and angles can help us better understand the shape and characteristics of cuboids.
3. There are four angles, all right angles:
A rectangle is a rectangle with four corners. Its opposite sides are equal, and all four corners are right angles. This feature has important applications in mathematics and geometry. For example, in a rectangle, the diagonal is the common side of two adjacent corners, and their lengths are equal. In a square, the diagonal is the common side of two adjacent corners, and their lengths are equal.
4. Symmetry:
A cuboid is symmetrical, which means that one part of a cuboid can overlap another part by rotating or flipping. These symmetries make cuboids very useful in the fields of mathematics, engineering and architecture. At the same time, the cuboid is also a central symmetrical figure, an axisymmetric figure, that is, symmetrical at the center point and symmetrical on the axis.
Second, the definition of rectangular length and width:
1. According to custom, the long side of a rectangle is called long and the short side is called wide.
2, and the horizontal plane in the same direction is called long, and vice versa. The length and width of a rectangle are relative, so we can't absolutely say "longer than wider".