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Geometry

Find 4 rectangles with same area with different perimeter?

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2013-02-04 23:47:12
2013-02-04 23:47:12

10cm by 10cm (perimeter=40cm),

5cm by 20cm (perimeter=50cm),

50cm by 2cm (perimeter=104cm),

100cm by 1cm (perimeter=202cm).

All of these rectangles' areas are 100cm2

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There is no relationship between the perimeter and area of a rectangle. Knowing the perimeter, it's not possible to find the area. If you pick a number for the perimeter, there are an infinite number of rectangles with different areas that all have that perimeter. Knowing the area, it's not possible to find the perimeter. If you pick a number for the area, there are an infinite number of rectangles with different perimeters that all have that area.


Not enough data. Different rectangles (different length:width ratios) can have the same area, but different perimeters.


There is no standard relationship between perimeter and area. For example, you can have two rectangles that have the same perimeter, but different 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.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.



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.


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.



Yes. Say there are two rectangles, both with perimeter of 20. One of the rectangles is a 2 by 8 rectangle. The area of this rectangle is 2 x 8 which is 16. The other rectangle is a 4 by 6 rectangle. It has an area of 4 x 6 which is 24.


Yes, it can because a 3 by 6 rectangle has the perimeter of 18 and has the area of 18! :)



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.


The area doesn't tell you the dimensions or the perimeter. It doesn't even tell you the shape. -- Your area of 36 cm2 could be a circle with a diameter of 6.77 . (Perimeter = 21.27.) -- It could be a square with sides of 6 . (Perimeter = 24.) -- It could be rectangles that measure 1 by 36 (Perimeter = 74) 2 by 18 (Perimeter = 40) 3 by 12 (Perimeter = 30) 4 by 9 (Perimeter = 26). There are an infinite number of more rectangles that it could be, all with the same area but different perimeters.


You would have to know what kind of figure you are talking about. For the same perimeter, you can have a different surface area, depending on whether you have a circle, a square, different kinds of rectangles, etc.


Perimeter: add all sides area: multiply length times width for rectangles


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.


The perimeter, for a given area, varies depending on the shape. It is different, for example, for a circle, for a square, and for rectangles of different length/width ratio.


That depends on the exact form of the block - whether it is square, or different forms of rectangles. The perimeter to area ratio is not the same for all shapes.


If the sides are in cm, then you would multiply the length of the shape by the width, which equals area. And area is in the unit of the sides but squared. So in this example it would be cm2. ========================================= The answer to the question is: You can't. The perimeter doesn't tell you what the area is. You can have two different drawings with the same perimeter and different areas, or with the same area and different perimeters. Even if they're both triangles, or both rectangles, etc. You can't take perimeter and 'work out' area from it.



You can't tell the perimeter from the area. There are an infinite number of different shapes,all with different perimeters, that have the same area. Even if you only consider rectangles,there are still an infinite number of those that all have the same area and different perimeters.Here are a few rectangles with area of 6 square feet:Dimensions ... Perimeter0.75 x 8 . . . . . . 17.51 x 6 . . . . . . . . 141.5 x 4 . . .. . . . 112 x 3 . . . . . . . . 10


A rectangle cannot really have the same area and perimeter because an area is a 2-dimensional concept while a perimeter is 1-dimensional.However, you can have rectangles such that the numericalvalue of their area and perimeter are the same.Take any number x > 2 and let y = 2x/(x-2)Then a rectangle with sides of x and y has an area and perimeter whose value is 2x2/(x-2)


To find the perimeter you add and to find the area we multiply.



You can't do that. For one thing, perimeter is a distance, and doesn't even havethe same units of measurement that area has. And for another thing, there's nodirect connection between area and perimeter. Knowing one of them doesn't tellyou the other one. You can name an area, and there are actually an infinitenumber of rectangles, all with different perimeters, that all have that much area.



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