a wire is in the shape of a square of side 10 cm . if the wire is rebent into a rectangle of length 12 cm . find the breadth which encloses more area the square or the rectangle 

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Given: Side of square = 10 cm

⇒ Length of wire = perimeter of square = 4 × 10 cm = 40 cm

Now since wire is rebent into rectangle

⇒ Perimeter of rectangle = length of wire

⇒ 2 (length + breadth) = 40 cm

Thus breadth of rectangle is 8 cm

also area of square = (10 cm)² = 100 cm²

and area of rectangle = 12 cm × 8 cm = 96 cm

Clearly, area of square > area of rectangle

Hence the square encloses more area.