Two rectangles with equal circumference, must they also have the same area?

Wrong. Two rectangles with equal circumference, their area is not necessarily equal. Suppose one of them is 10 centimeters long and 5 centimeters wide.

Then the area of this rectangle is 10 5 = 50 square centimeters. Suppose a rectangle is 12 centimeters long and 3 centimeters wide, then the area of this rectangle is 12 3 = 36 square centimeters. 50 square centimeters is not equal to 36 square centimeters, so two rectangles with equal circumferences are not necessarily equal in area.

Data expansion: A rectangle, also known as a rectangle, is a flat figure, which is a parallelogram with an angle of right angles. A rectangle is also defined as a parallelogram with all four corners at right angles. A square is a special rectangle with four sides of equal length.

The nature of the rectangle is: two diagonal lines are equal; The two diagonals are bisected with each other; The two sets of opposite sides are parallel to each other; The two sets of opposite sides are equal; All four corners are right angles; There are 2 axes of symmetry (4 for squares); It is unstable (easily deformed); The square of the diagonal length of the rectangle is the sum of the squares of the two sides; The quadrilateral obtained by sequentially connecting the midpoints of each side of the rectangle is a diamond.

Determination of the rectangle:

1. There is a parallelogram with a right angle that is a rectangle.

2. A parallelogram with equal diagonals is a rectangle.

3. A parallelogram with adjacent sides perpendicular to each other is a rectangle.

4. A quadrilateral with three corners that are right angles is a rectangle.

5. Quadrilaterals with equal diagonals and bisected from each other are rectangular.

This answer is wrong, two rectangles of equal area do not necessarily have the same circumference.

For example, the two rectangles below, <>

They both have an area of 24 square centimeters, but their circumferences are not equal.

Circumference of the first rectangle: (6 4) 2 = 20 (cm) Circumference of the second rectangle: (8 3) 2 = 22 (cm).

Two rectangles with equal circumference, their area is not necessarily equal.

Using a hypothetical approach, assuming that the circumference of the two rectangles is 24 cm, one rectangle is 8 cm long and 4 cm wide, and the other rectangle is 7 cm long and 5 cm wide.

1) The length of a rectangle is 8 cm, the width is 4 cm, and the area is: 8 4 = 32 (square centimeters).

2) the length of the other rectangle is 7 cm and the width is 5 cm; 7 5 = 35 (square centimeters).

The area of the rectangle (2) is greater than the area of the rectangle (1).

The properties of the rectangle are:

The two diagonal lines are equal; The two diagonals are bisected with each other; The two sets of opposite sides are parallel to each other; The two sets of opposite sides are equal; All four corners are right angles; There are 2 axes of symmetry (4 for squares);

It is unstable (easily deformed); The square of the diagonal length of the rectangle is the sum of the squares of the two sides; The quadrilateral obtained by sequentially connecting the midpoints of each side of the rectangle is a diamond.

Analysis: If the circumference of two rectangles is equal, the smaller the difference between length and width, the larger the area, and when the length and width are equal, the area of Qi Zao is the largest (square) This is the solution

Solution: An example can be given when the circumference of a rectangle is 24 cm:

One is 10 centimeters long, 2 centimeters wide, and has an area of 20 square centimeters;

the other is 8 centimeters long, 4 centimeters wide, and has an area of 32 square centimeters;

It is very obvious that 20 square centimeters is not equal to 32 square centimeters Therefore, it is wrong to say that two rectangles with equal circumferences must have equal areas of dust and silver

Not necessarily equal.

Because the circumference of the rectangle = (length + width) x2

The area of the rectangle = length x width.

For example, if the length of a rectangle = 5 and the width = 4, calculate its circumference = (4 + 5) x 2 = 18 and area = 4x5 = 20 according to the formula

The length of a rectangle = 3 and the width = 6, according to the formula, calculate its circumference = (3 + 6) x 2 = 18 area = 3x6 = 18

The length of a rectangle = 2 and width = 7, and its circumference = (2+7)x2=18 and area = 2x7=14 according to the formula

From the above examples, it can be concluded that the circumference of the rotten shape of the rectangular servant is cautious, and their area is not necessarily equal.

Two rectangles with equal circumference, a certain area equal?

The areas are not necessarily equal. This is a false proposition.