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 its breadth. Which encloses more area, the square or the rectangle and by how much?

Given:

Side of square = 10 cm

Length of rectangle = 12 cm

Length of wire = Perimeter of square

= 4 × side

= 4 × 10

= 40 cm

Since the wire is rebent into a rectangle,

Perimeter of rectangle = Length of wire = 40 cm

Perimeter of rectangle = 2(length + breadth)

⇒ 40 = 2(12 + breadth)

⇒ $\dfrac{40}{2}$ = 12 + breadth

⇒ 20 = 12 + breadth

⇒ breadth = 20 - 12

⇒ breadth = 8 cm

Area of square = side × side

= 10 × 10

= 100 sq. cm

Area of rectangle = length × breadth

= 12 × 8

= 96 sq. cm

Since 100 sq. cm > 96 sq. cm, the square encloses more area.

Difference in areas = 100 - 96 = 4 sq. cm

Hence, the breadth of the rectangle is 8 cm and the square encloses more area than the rectangle by 4 sq. cm.