Good Question !
the perimeter is constant but the diagonal will become twice the side of the square . If the length of the diagonal increases then the distance between those two sides joining the diagonal will keep on decreasing thus if the diagonal becomes twice the side then the angle between those two sides will become 180°, hence a straight line and the same will happen with the two othe sides the 3 straight lines will be formed coinciding each other.
The 3 sides will be the
1) the two sides
2) The diagonal
3) The other two sides
Hence , if all the three sides will coincide with each other then,
The resultant figure will be a line whose length will be equal to the twice the side . And the Area will be equal to 0 ( zero ).
THIS QUESTION TESTS THE IMAGINATION POWER NOT THE MATHEMATICAL ABILITY
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