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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)

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โˆ™ 2011-10-06 13:13:37
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Q: What are some rectangles with the area the same as the perimeter?
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Do all rectangles with the same perimeter have the same area?

No. Here are four rectangles with the same perimeter:1 by 6 . . . . . perimeter = 14, area = 62 by 5 . . . . . perimeter = 14, area = 103 by 4 . . . . . perimeter = 14, area = 1231/2 by 31/2 . . perimeter = 14, area = 121/4With all the same perimeter . . . -- The nearer it is to being square, the more area it has.-- The longer and skinnier it is, the less area it has. If somebody gives you some wire fence and tells you to put it uparound the most possible area, your first choice is to put it up ina circle, and your second choice is to put it up in a square. Rectanglesare out, if you can avoid them.

Two rectangles have a perimeter of 16 inches Name one possible area for each rectangle?

* It is unclear if the question is asking about two rectangles, each with a perimeter of 16, or two rectangles whose perimeters sum to 16. This answer assumes the former.Other than the 4x4 square, which coincidentally has both a perimeter and area of 16, some examples would be:1 x 7 rectangle : perimeter 16 in. , area 7 sq. in2 x 6 rectangle : perimeter 16 in., area 12 sq. in3 x 5 rectangle: perimeter 16 in., area 15 sq. inYou can calculate that for a given perimeter, the largest area is found in the square with a side measurement of P/4, i.e. the length and the width are the same.

If 2 rectangles have the same area will they always be similar?

No some times

What are some sketches of rectangles with a perimeter of 120?

10 by 50, 15 by 45, 20 by 40.

Do the rectangular parallelogram both have the same area explain why or why not?

No. A rectangle and a parallelograms are desciptions of quadrilateral shapes. There is no indication of the size of either. So some rectangles are smaller than some parallelograms and some parallelograms are smaller than some rectangles.

Why won't squaring a side work with all rectangles to find the area?

Some rectangles don't have equal sides.

Do some rectangles have 4 sides the same length?

Yes, they are called squares. Squares are a subset of rectangles.

What does perimeter and area have in common?

One thing that area and perimeter has in common is that they both measures some part of a shape

What jobs use area and perimeter?

Some of the jobs that use area and perimeter include surveying, drafting and construction.

What jobs use perimeter and area?

Some of the jobs that use area and perimeter include surveying, drafting and construction.

Why are areas and perimeter not dependent on one another?

That's because you can easily have two different shapes with the SAME perimeter, and DIFFERENT areas, or vice versa. Here is an example:* A 2x2 rectangle has an area of 4, and a perimeter of 8. * A 1x3 rectangle has an area of 3, and a perimeter of 8. * A 0x4 rectangle has an area of 0, and a perimeter of 8. (If you don't like this rectangle, you can make one that is arbitrarily close, i.e., a very small width.) Note that for two SIMILAR figures, any linear measurements are proportional to the scale size, and any area measure is proportional to the square of the scale size - that will make the area proportional to the perimeter, but only for two similar shapes, e.g., two rectangles with the same length-to-width ratio.

What are the rectangles that have the same perimeter as area?

Perimeter is a length, and a length cannot be the same as an area.Ignoring the units, all rectangles that have the same numerical perimeter as area are those that satisfy:2 x (length + width) = length x widthwhich can be rearranged to give:width = 2 x length/(length - 2)Meaning that given any length over 2, a width can be found to give a rectangle that meets the requirement that its numerical perimeter is the same as its numerical area. (For a length greater than 0 and less than 2, the width would be negative and not possible; similarly for a length less than 0, the length is negative and not possible. When the length is 2, the width is undefined and so not possible. When the length is 0 the width is 0 and it is not a rectangle.)At some stage as the length increases, the length will equal the width and as the length continues to increase the rectangle then given will match the previous rectangles with the length and widths swapped. This occurs when:length = 2 x length/(length - 2)⇒ length x (length - 4) = 0⇒ length = 4.So, as long as the length is greater than or equal 4 it will be the longer side - the length, by convention, is the longer side. Thus all rectangles satisfy:width = 2 x length/(length - 2)with length ≥ 4, will have the numerical value of their perimeter the same as the numerical value of their area.For example:4 cm x 4 cm: perimeter = 16 cm, area = 16 cm25 cm x 31/3 cm: perimeter = 162/3 cm, area = 162/3 cm26 cm x 3 cm: perimeter = 18 cm, area = 18 cm241/2 cm x 33/5 cm: perimeter = 161/5 cm, area = 161/5 cm2etcNote: the first example is a square which is a rectangle with all the sides the same length.

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