Imagine that we are taking a wire piece and shaping it into a rectangle. Then we are shaping it into a square. In both cases will the area be same? If not why? And what about perimeter?

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Solution

$Let the length of wire piece = x Now if we are shaping it into a rectangle then the perimeter of rectange will be equal to length of wire peice . 2 (l + b) = x . . . . . (1) Now if we are reshaping it into a square then then the perimeter of square will be equal to length of wire peice . 4 \times side = x . . . . (2) So side = \frac{x}{4} unit So we can say that perimeter will be same . Now area of square = {side}^{2} = \frac{x^{2}}{16} But we cannot find area of rectange because we do not know the length and breadth of rectange .$

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