Sep 28, 2017

If area of a square is equal to the area of a rectangle. Is perimeter be equal also?

Equal area of square and rectangle will never have equal perimeter.

This can be illustrated with formula and with a an example.

Let side of a square be x.
Let the length and breadth of a rectangle be l and b whose area is equal to the area of the square.
 area of a square is equal to the area of a rectangle. Is perimeter be equal also
I am taking few value of side of the square and taking the equal area the length and breadth are set a value.
Case 1:
let x=2

Therefore X2 = 4
Let l=4
and b=1
So that the area remain same.
suppose the perimeter of the rectangle be greater than the perimeter of the square.
Therefore
2(l+b)-4x will be positive.
2(4+1)-4*2
=10-8
=2

Case 2:
let x=4

Therefore X2 = 16
Let l=8
and b=2
So that the area remain same ie 16 unit.
Let check again:
2(l+b)-4x will be positive.
2(8+2)-4*4
=20-16
=4

Case 3:
let x=8

Therefore X2 = 64
Let l=16
and b=4
So that the area remain same ie 64 unit.
Let check again:
2(l+b)-4x will be positive.
2(16+4)-4*8
=40-32
=8

Therefore in all three cases we noticed that the perimeter of the rectangle is always positive.

Therefore if the area of a square and that of a rectangle are equal then the perimeter of the rectangle will always be greater.

Please comment if you are satisfied with the answer.


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