Who helps to say an example of a rectangle with different shapes having the same circumference and e

Let the length and width of the rectangle be a and b respectively, then the area is ab.

The length and width of another rectangle with different shapes and equal circumferences are (a-n) and (b+n), respectively, then the area is (a-n) (b+n).

ab+an-bn-n

When the area is equal, ab=ab+an-bn-n

an-bn-n

n(a-b-n)=0

Because the shape is different, n≠0. Rule.

a-b-n=0 i.e.

n=a-b, the length of another rectangle is a-n=a-(a-b)=a-a+b=b, and the width of the other rectangle is b+n=b+(a-b)=b+a-b=a=a, but the original rectangle is rotated 90°.

Let the two sides of the first open square be A1, the two sides of the second rectangle be A2, and B2.

a1+b1=a2+b2

a1*b1=a2*b2

Square the two sides of the first formula and substitute it into the second formula, so we get a1 2+b1 2=a2 2+b2 2, so the two rectangles that meet this formula are equal in circumference and equal in area.

No, let the length be x, the width be y, x = y, the area be b, and the perimeter be a.

x+y=axy=b

The solution of the equation is unique.

None of them have the same circumference, the circle area is the largest, and the shape is different, and the area is different.

Upstairs Let's take a look at the specific data, and see it in the long run!

Not equal. Analysis: You can set a specific value to make it easy to judge, and set the length of the rectangle to be 6 cm and the width to be 4 cm.

The side length of the square is 5, the circumference of the rectangle is: 2x(4+6)=20 cm, and the area is: 4x6=24 square centimeters.

The circumference of the square is: 4x5 = 20 cm, and the area is: 5x5 = 25 square centimeters.

From this, it can be seen that the circumference of the rectangle and the square are equal, but the area is not equal. Therefore, the proposition is wrong!

Perimeter formula. Circle: C = D = 2 R (D is the diameter, R is the radius, ) Circumference of the triangle c = A+B+C (ABC is the three sides of the triangle) Quadrilateral: C = A+B+C+D (ABCD is the length of the sides of the quadrilateral) Rectangle:

c = 2 (a + b) (a is long, b is wide) square: c = 4a (a is the length of the sides of the square).

Polygon: c = sum of all edge lengths.

The perimeter of the fan: c = 2r+n r 180 (n=central angle) = 2r+kr (k=radian).

A rectangle and a square have equal circumferences and their areas are not equal. The area of a square is larger than that of a rectangle. For example, the circumference is 36 cm.

Square area: 36 4 = 9 (cm).

9x9 = 81 (square centimeters).

The area of the rectangle: 10 cm long, 8 cm wide, and 36 cm in circumference, but the area is: 10x8 = 80 (square centimeters).

The area is not the same.

Let the side length of the square be a

This can be done with a rectangle with side lengths of a+t and a-t

The square of a (a-t) * (a+t) = a square - the area of the square of t is large.

No. Two rectangles with equal circumferences are not necessarily equal in area, not necessarily unequal.

For example, a rectangle with a length of 6 and a width of 2 and a rectangle with a length of 5 and a width of 3 have the same circumference but not the same area; Two rectangles with a length of 5 and a width of 3 have the same circumference and equal area.

The circumferences are equal, and the corresponding sides are equal in length, so that the area of the two rectangles is equal.

The circumferences are equal, and if the corresponding sides are not equal, then the areas of the two rectangles are not equal. For example, a rectangle is 6 long and 3 wide; The other rectangle is 5 long and 4 wide, and although their perimeters are equal, they are not equal because the corresponding sides are unequal in length, and the areas are 18 and 20 respectively.

Two rectangles with equal circumferences can have equal areas. For example, two long sides with equal short and long sides have equal areas of equal area.

It is possible that two rectangles with equal circumferences may not be equal in area.

Such as: the long side is 5 cm, the short side is 3 cm, the circumference is 16 cm, and the area is 15 square centimeters.

The long side is 6 cm, the short side is 2 cm, the circumference is 16 cm, and the area is 12 square centimeters.

Not necessarily.

The circumferences are equal, and the areas of the two rectangles corresponding to the same side lengths are also equal.

For example, if the corresponding sides of two rectangles are 5 meters long and 3 meters wide, then the area of both of them is equal to l5 square meters.

Two rectangles with equal circumferences are not necessarily equal in area, and I will not talk about the same situation.

For example, if the circumference is 12cm, then as long as the length and width = 6 (cm) are satisfied.

If the length is 5cm, the width is 1cm, and the area is 5cm.

If the length is 4cm, the width is 2cm, and the area is 8cm.

So the circumference of the two rectangles is the same, and the area is not necessarily equal.

Examples of rectangles with equal circumference and equal area?

Let the two sides of the first open square and the two sides of the circle be a1, and the two sides of the first cavity and the two rectangles of the first cavity are a2, and b2 then a1+b1=a2+b2 a1*b1=a2*b2 square the two sides of the first formula and substitute them into the second formula to obtain a1 2+b1 2=a2 2+b2 2, so the circumference of the two rectangles satisfying this formula is equal and the area is also equal.

There are two situations where the circumference is equal: one is the length of the self-length and the width are equal

Square; Two dus are not equal in length and width

But rectangular with equal circumference. The first DAO case is of course equal in size: in the second case, the area is absolutely unequal.

For example, if the circumference is 20 cm, (assuming that both length and width are integers) then there are many rectangles that meet this condition: 1 and 9 for length and width, 2 and 8, 3 and 7 respectively, etc

Although their circumference is equal, their area is not equal.

If the edge length of the original rectangle is A, and B is Bai2(A+B).

The area is a*b

If the length of one side of the rectangle is changed to a+c, since the circumference of zhi should be kept unchanged, the other side is: b-c, and the area is: (a+c)*(a-c).

The difference between the area of the original rectangle is: (a+c)*(b-c)-ab=bc-ac-c*c=c*(b-a-c), if the result is equal to 0, only when b=a+c is true, that is, the rectangle with a side length on one side and a+c on the other side is a+c.

The length of one side is a+c, and the other side is: a+c-c has the same circumference and area.

And these two rectangles are exactly the same.

Therefore, there are no two rectangles with equal circumference.

The circumference is equal, that is, the sum of length and width is also equal, but the value of length and width is not unique, so the shape of the rectangle cannot be determined

So the answer is: false

For example, a rectangle with a length of 4 cm, a width of 3 cm, and a circumference of 14 cm;

The other is 6 centimeters long, 2 centimeters wide, and 16 centimeters in circumference, and they are all 12 centimeters in size

Therefore, the statement that two rectangles with unequal circumferences may also have equal areas is true, so the answer is:

For example, a rectangle with a length and width of , with a circumference of 22 and an area of 30;

The length and width of the rectangle collapse are clear, and the circumference is 22 and the area is 10