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How can two rectangles have the same area and different perimiters?
Wiki User
∙ 13y ago
It could happen. For Example: If one of the sides is 4 inches and the other is 3 inches--
Area: 12
Perimeter: 18
But if one side is 2 inches and the other is 6 inches:
Area: 12
Perimeter: 16
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I think the questioner knows it happens, and is wondering why it happens.
You may have heard this, but it will make sense intuitively even if you haven't. A soap bubble is a sphere because it is the natural shape that has the smallest surface area that the gas within can take. What force would there normally be keeping a single free-floating bubble in any shape other than a sphere? In your mind, stretch a bubble out to be any shape other than a sphere, and you will sense that the new shape can't be sustained by nature; natural forces will bring the bubble back to a sphere. Under ordinary circumstances you have never seen a bubble that is not a sphere, or that is not tending toward a sphere-like shape given other limiting factors, like the bubble resting on the surface of water, or bubbles grouped together.
It won't be surprising then that a circle of a given area will have a circumference a little smaller than the perimiter of a square with the same area. A circle with radius=1 will have an area of pi square units. A square that has one side equal to the square root of pi will have an area of pi square units. The circumference of a circle is equal to pi times the diameter (2 X the radius). So our circle has a circumference of 6.28318. The square of equal area will have a perimiter of 4(square root of pi), or 7.08981. You will get similar results comparing the surface areas of a sphere and a cube of equal volume.
In the plane geometry of rectangles exclusively, a square with 32 units on one side will have an area of 1024 square units. If a rectangle has 8 units on one side the other side has to be 128 units to come to an area of 1024, for a perimiter of 272 units. If a rectangle is 4 units on one side, the other side must be 256 units to come to an area of 1024, and the perimiter is 520. If one side is .5 units long, the other side must be 2048 units, and the perimiter is 4097 units!
Think of it this way. Visualize a square. In the square, every unit of width distributes the same 'area' across every unit of height, and every unit of height distributes the same 'area' across every unit of width; there is an efficient distribution of area across dimensions (if you want your final shape to remain a square), not unlike a bubble that pulls itself by natural forces into the smallest ratio of surface area to volume.
Another way of thinking about this: Length of perimiter is, obviously, a linear measure-- you are adding the lengths of lines. Lines have one dimension in Euclidean geometry. Take a line parallel to the y axis and that is arbitrarily long (as long as you want to imagine it). So far there is no area whatsover, right? By extending a line from the base and parallel to the x axis, you can define a rectangle with an area arbitrarily close to zero, or approaching infinity. The area of a shape is not necessarily proportional to the lengths of any of the sides of the shape.
Wiki User
∙ 13y ago
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What is the perimeter of a rectangle whose area is 21?
That depends on the rectangle! You can have different rectangles with the same area, but with different perimeters.
If the area of the rectangle is 320cm squared find its perimeter?
Not enough data. Different rectangles (different length:width ratios) can have the same area, but different perimeters.
What is the perimeter in meters of a 28 acre field?
The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.
Why does rectangles have the same area and perimeter?
they dont
How many rectangles have the same area and perimeter of 18?
thare is only 1 differint rectangles
Do two different rectangles with the same perimeter necessarily have the same area?
no
Can different rectangles have the same area and perimeter?
It's very easy for two rectangles to have the same area and different perimeters,or the same perimeter and different areas. In either case, it would be obvious toyou when you see them that there's something different about them, and theywould not fit one on top of the other.But if two rectangles have the same area and the same perimeter, then to look at themyou'd swear that they're the same rectangle, and one could be laid down on the otherand fit exactly.
What is the perimeter of a rectangle whose area is 21?
That depends on the rectangle! You can have different rectangles with the same area, but with different perimeters.
If the area of the rectangle is 320cm squared find its perimeter?
Not enough data. Different rectangles (different length:width ratios) can have the same area, but different perimeters.
What is the perimeter in meters of a 28 acre field?
The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.
Is there an example of 2 rectangles with the same area but different areas?
No. Many investigators have searched for such an example, but none have found it yet. According to all published research so far, two rectangles with the same area always have the same area. But the search goes on, in many great universities.
Why does rectangles have the same area and perimeter?
they dont
How do you convert perimeter into square meters?
There is no standard relationship between perimeter and area. For example, you can have two rectangles that have the same perimeter, but different area.
How many rectangles have the same area and perimeter of 18?
thare is only 1 differint rectangles
If two rectangles have the same area do they also have to have the same perimeter?
Not necessarily. Let's say that there is a circle with the area of 10. Now there is a star with the area of 10. They do not have the same perimeter, do they? That still applies with rectangles. There might be a very long skinny rectangle and a square next to each other with the same area, but that does not mean that they have the same perimeter. Now if the rectangles are congruent then yes.
Draw 2 rectangles with same perimeter but difference area?
This browser is hopeless for drawing but consider the following two rectangles: a*b and (a+1)*(b-1). Their perimeter will be 2a+2b but unless a = b-1, their area will be different.
Is the area the same on all rectangles with the same perimeter?
No, it is not. I'll give you two examples of a rectangle with a perimeter of 1. The first rectangle has dimensions of 1/4x1/4. The area is 1/16. The second rectangle has dimensions of 3/8x1/8. The area is 3/64. You can clearly see that these two rectangles have the same perimeter, yet the area is different.
