A metallic wire is first bent in the shape of a square and then into a rectangle. If the length and breadth of the rectangle are 27 cm and 13 cm respectively, then the area of the square is ___ (in sq. cm)

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Solution

Since the same wire is reshaped into both square and rectangle, the perimeter of both the shapes is same.

Perimeter of square = $4 \times s i d e$

Perimeter of rectangle = $2 \times (l e n g t h + b r e a d t h)$

= $2 \times (27 c m + 13 c m)$

= $80 c m$

On equating the perimeters,

$4 \times s i d e = 80 c m$

$s i d e = 20 c m$

$A r e a o f t h e s q u a r e = 20 c m \times 20 c m = 400 s q . c m .$

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A metallic wire is first bent in the shape of a square and then into a rectangle. If the length and breadth of the rectangle are 27 cm and 13 cm respectively, then the area of the square is _____ (in sq. cm) ___

A metallic wire is first bent in the shape of a square and then into a rectangle. If the length and breadth of the rectangle are 27 cm and 13 cm respectively, then the area of the square is ___ (in sq. cm)

_