Question

a wire is in the shape of square of 10 centimetre if a wire is Re bent into a rectangle of length 12 cm find its breadth which figure and close more area and by how much

Answer 1

Find the length of the wire:

Length = 10 cm

Perimeter = 10 x 4 = 40 cm

⇒ The length of the wire is 40 cm

Find the breadth of the rectangle:

Perimeter = 40 cm

Length = 12 cm

Perimeter = 2 (Length + Breadth)

40 = 2( 12 + Breadth)

20 = 12 + Breadth

Breadth = 20 - 12 = 8 cm

Find the area of the square:

Area = Length x Length

Area = 10 x 10 = 100 cm²

Find the area of the rectangle:

Area = Length x Breadth

Area = 12 x 8 = 96 cm²

Compare:

100 cm² > 96 cm²

⇒ Area of square is bigger

Difference = 100 - 96 = 4 cm²

Answer: The breadth of the rectangle is 8 cm. The area of the square is bigger than the area of the rectangle by 4 cm²

Answer 2

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Side of a square = 10cm

⠀⠀⠀Perimeter of square = 4 × S

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 4 × 10 = 40cm².

Perimeter of sq. = Perimeter of rectangle =40cm²

Perimeter of rectangle = 2 ( L + B )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀40 = 2 ( 12 + B )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀40 = 24 + 2B

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀40 - 24 = 2B

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀B = $\frac{16}{2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀B = 8cm.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Area of sq. = S × S

⠀⠀⠀⠀⠀⠀⠀= ( 10 × 10 ) cm²

⠀⠀⠀⠀⠀⠀⠀= 100 cm²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Area of rectangle = ( L × B ) sq. unit

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = ( 12 × 8 ) cm²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 96 cm².

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Square has encloned more area by 4cm² .