Question

A wire is in the shape of a rectangle Its length is 36 cm and breadth is 18 cm. If the same wire
is rebent in the shape of a square, what will be the measure of each side? Also find which shape
encloses more area.​

Answer 1

Given that,

• Length of a rectangular wire = 36cm

• Breadth of a rectangular wire = 18cm

Let's find the perimeter of the rectangle =

⇒ Perimeter of the Rectangle = 2(Length + Breadth)

⇒ Perimeter = 2(36cm+18cm)

⇒ Perimeter = 2(54cm)

⇒ Perimeter = 108cm

∴ The perimeter of the Rectangle is 108cm.

If the same wire is bent into a square then the perimeter of the Rectangle is equals to the perimeter of square

⇒ Perimeter of the Square = 4(side) = 108cm

⇒ 4(side) = 108cm

⇒ side = 108cm/4

⇒ side = 27cm

∴ The side of the square is 27cm.

• Let's find the area of both rectangle and the square.

Area of the Rectangle =

⇒ Length × Breadth

⇒ 36cm × 18cm

⇒ 648 cm²

Area of Square =

⇒ (Side)²

⇒ (27cm)²

⇒ 729 cm²

∴ The square has greater area than the rectangle.

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Answer 2

Given that,

Length of a rectangular wire = 36cm

Breadth of a rectangular wire = 18cm

Let's find the perimeter of the rectangle =

⇒ Perimeter of the Rectangle = 2(Length + Breadth)

⇒ Perimeter = 2(36cm+18cm)

⇒ Perimeter = 2(54cm)

⇒ Perimeter = 108cm

∴ The perimeter of the Rectangle is 108cm.

If the same wire is bent into a square then the perimeter of the Rectangle is equals to the perimeter of square

⇒ Perimeter of the Square = 4(side) = 108cm

⇒ 4(side) = 108cm

⇒ side = 108cm/4

⇒ side = 27cm

∴ The side of the square is 27cm.

Let's find the area of both rectangle and the square.

Area of the Rectangle =

⇒ Length × Breadth

⇒ 36cm × 18cm

⇒ 648 cm²

Area of Square =

⇒ (Side)²

⇒ (27cm)²

⇒ 729 cm²

∴ The square has greater area than the rectangle.

Hope this helps you.

Thankyou for your question.

Mark me as brainleist.