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To answer that question, look at the formulas for both Let's take a rectangle with length L and width W. The area is LW and the perimeter is 2L+2W

So can LW=2L+2W

Solve for L LW/2=L+W 1/2L(w-2)=w L=(2w)/(W-2)

This tells us the answer is YES. But it also tells us W must be greater than 2. Try W=3, this gives us L= 6/1=6 So look at a 6x3 rectangle Area is 18 and perimeter is 12+6=18

True, but there is an important caveat. The numbers, for the area and perimeter, can be the same but the two cannot be the same. The simple reason is that the area will be in square units whereas the perimeter will be in linear units. The consequnce of this is that if the units of measurement are changed (eg from centimetres to metres, or inches) the equality in numbers will no longer hold.

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โˆ™ 2011-03-09 12:46:41
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Q: Can a rectangle's area be the same as the perimeter?
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Related questions

Why does rectangles have the same area and perimeter?

they dont

Do two different rectangles with the same perimeter necessarily have the same 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.

Can a rectangles perimeter be the same as the area?

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

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.

Find 4 rectangles with same area with different perimeter?

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

What are some rectangles with the area the same as the perimeter?

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)

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.

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.

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.

Can two rectangles to have the same area without the same perimeter?

Yes. Take a simple rectangle of 1cm x 6cm. It's area is 6cm2 and its perimeter is 14cm. Now - a rectangle if 2cm x 3cm has the same area, but has a perimeter of just 10 Centimetres !

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