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Let's say the side length of a square is x. The square's area is just x2, and its perimeter is 4x. If we want the perimeter to be equal to the area, 4x = x2, so x = 4.

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Q: A square may have the same numerical value for its area and perimeter?
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Is the perimeter always smaller than the area?

The perimeter is in linear units (e.g. meters), and the area in square units (e.g. square meters), so you can't compare them directly. If you insist on comparing a square unit with a linear unit - even though this has no physical significance! - it all depends on the units chosen, and the size. A square of 1x1 has a surface area of 1 square unit, but a perimeter of 4 units. This is a counterexample to your proposition. At a size of 4x4, you reach the "break-even point"; above that, the perimeter would have a lower numerical value than the area. But please note that if you use physical measurements, the square of 1 meter x 1 meter (for example) has a perimeter of 4 meters and an area of 1 square meter (perimeter has a higher numerical value), but when you change units to centimeters, the same square has a perimeter of 400 cm, and an area of 10,000 cubic centimeters (here, the perimeter has a LOWER numerical value).


What is the length of one side of the square whose perimeter has the same numerical value as its area?

If the side of the square is X then we are going to have 4x=x2 From this equation we get x=4


A shape with the same area and perimeter?

As a perimeter is a measure of length and has different units to those measuring an area then it is the numerical value that is the same. CIRCLE : area = perimeter occurs when πr2 = 2πr = : r = 2 SQUARE : area = perimeter when d2 = 4d : d = 4, where d is the length of a side.


Why the area and the perimeter of a figure can never be equal?

The area and perimeter cannot be equal because the perimeter is a linear measure while an area is a square measure. However, it is perfectly possible for them to have the same numerical value. For example, a 3cm by 6 cm square has a perimeter of 2*(3+6) = 18 cm and an area or 3*6 = 18 sq cm.


Value of a perimeter be rational or irrational?

Either. The perimeter of a square with area 1 square unit is 4, a rational value. The perimeter of a square with area 2 square unit is 4*sqrt(2), an irrational value.


Is it possible for the perimeter to be the same numerical value as the area on a irregular shape?

Noyou must have did something wrong


A square has an area of 400 what is the perimeter?

A square with an area of 400 square units has a perimeter of 80 units.


The larger the perimeter of a square the larger the area of that square?

The area of a square is a function of the perimeter of the square.


What is the perimeter of a square with an area of 49?

The area of square is the square of one of its sides, which are all equal. To find the value of a side, take the square root of the area. In this case the square root of 49cm2 is 7cm. The perimeter is the sum of all four sides of the square, so the perimeter of a square with an area of 49cm2 is 7+7+7+7 = 28, or 4x7 = 28.


What is length of the side of a square if its perimeter and area have the same value?

4 units


If the area of a square is 12 what is perimeter?

If the area of a square is 12 the perimeter is: 13.86


What is the perimeter of a square that has an area of 49 cm squared?

The area of square is the square of one of its sides, which are all equal. To find the value of a side, take the square root of the area. In this case the square root of 49cm2 is 7cm. The perimeter is the sum of all four sides of the square, so the perimeter of a square with an area of 49cm2 is 7+7+7+7 = 28, or 4x7 = 28.