It is possible to have a shape such that its perimeter is numerically equal to its area?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
There's a conceptual mistake in this question! A perimeter is measured as length thus in, say, meters, and the area in sq. Meters. They can never de equal! E. Cruz
Can you show that no matter what the shape is, we can always find a suitable case where perimeter = area? E.g. what if we were considering an equilateral triangle?
For every polygon, there is a possibility that area is same as perimeter.
Take for example, a square with length 4, area = perimeter = 16 .
Take a equilateral triangle with length a = 1 2 3 , area = perimeter = 0 . 5 7 7 …
consider a square with side length 4. 4X4=16. 4+4+4+4=16. Therefore p-a=0
Actually if you consider the unit of measurement, and ignore all line, then the answer must be false.
A circle with radius = 2 also works
Problem Loading...
Note Loading...
Set Loading...
Let P = perimeter of a square, A = area of a square and s = side
P = 4 s
A = s 2
If P = A , then s 2 = 4 s
s 2 − 4 s = 0
s ( s − 4 ) = 0
H e n c e s = 0 , s = 4 .
As s = 4 is a solution of a square ( s = 0 can be ignored), and a square is a shape, regardless of all other shapes the answer must be T R U E