Question

A wire is in the shape of a rectangle. Its length is 40 cm and Breadth is 22 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

$\huge {\mathcal{\underline \green{Question}}}$

A wire is in the shape of a rectangle. Its length is 40 cm and Breadth is 22 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 ?

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$\huge\boxed{Given :}$

➣ First a wire is bent in the shape of a rectangle and after it is rebent to form a square.

➣ Length of the Rectangle = 40 cm

➣ Breadth of the Rectangle = 22 cm

$\huge\boxed{To\: Find \: :}$

➣ Side of Square

➣ The Shape Which encloses more area

$\huge\boxed{Solution :}$

➪ Perimeter of Rectangle = 2(Length + breadth)

⇒Perimeter of rectangle = 2(40 + 22)

⇒Perimeter of Rectangle = 2 × 62

⇒Perimeter of Rectangle = 124 cm

➣ Perimeter of Rectangle = 124 cm

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➣ Perimeter of Square = 124 cm

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➪ Perimeter of Square = 4 × Side

$➪ \: side \: = \frac{perimeter}{4}$

$⇒ \: side \: = \cancel\frac{124}{4}$

⇒Side = 31 cm

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➣ Side of Square = 31 cm

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➪ Area of Rectangle = Length × Breadth

⇒ Area of Rectangle = 40 × 22

⇒ Area of Rectangle = 880 cm²

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➪ Area of Square = (side)²

⇒ Area of Square = (31)²

⇒ Area of Square = 961 cm²

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➣ So, The measure of each Side of Square is 31 cm.

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➣ Area of Square encloses more Area than the Area of Rectangle.

Answer 2

Answer:

Side of square measures 31 cm and area of square encloses more area than the area of rectangle.