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.

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 X^{2} = 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 X^{2} = 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 X^{2} = 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.