Question

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

Answer:

AnswEr :

Question states that, a wire is in the shape of a rectangle whose Length (l) is 40 cm and Breadth (b) is 22 cm and that wire is converted from rectangle to square. So, there will be no change in the length of the wire and hence, Perimeter of rectangle is equal to perimeter of square. mathematically :

Perimeter of rectangle = Perimeter of square

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• P E R I M E T E R O F S Q U A R E :

↠ Perimeter of square = 4 × Side

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•P E R I M E T E R O F R E C T A N G L E :

↠ Perimeter of rectangle = 2(Length + Breadth)

↠ Perimeter of rectangle = 2(40 + 22)

↠ Perimeter of rectangle = 2(62)

↠ Perimeter of rectangle = 124 cm

∴ The Perimeter of rectangle is 124 cm.

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• According to the Question :

↠ Perimeter of rectangle = Perimeter of square

↠ 124 = 4 × side

↠ 124 ÷ 4 = side

↠ a = 31 cm

∴ The side of the square is 31 cm.

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• A R E A O F R E C T A N G L E :

↠ Area of rectangle = Length × Breadth

↠ Area of rectangle = 40 × 22

↠ Area of rectangle = 880 cm²

∴ The area of rectangle is 880 cm².

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• A R E A O F S Q U A R E :

↠ Area of square = (Side)²

↠ Area of square = (31)²

↠ Area of square = 961 cm²

∴ The area of square is 961 cm².

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∴ The area of square encloses more area then area of rectangle by 81 cm².

Answer 2

Step-by-step explanation:

☞Answer:-

Given:-

• Length of the square is 40cm.
• Breadth of the square is 22cm.

To find:-

• Area of the square

Solution:-

Length= 40cm

Breadth= 22cm

Perimeter of the rectangle= Length of the wire

=2(l+b)= 2(40cm + 22cm)

=2 × 62cm = 124cm

Now, the wire is rebent into a square.

Perimeter= 124cm

4 × side = 124

$Therefore \: side \: =  \: \frac{124}{4} cm \: = \: 31cm.$

So, the measure of each side= 31cm

$Area \: of \: rectangular \: shape \: = \:  l \: \times \: b$

$= \: 40cm \: \times \: 22cm$

$= \: 880cm {}^{2}$

Area of a square shape = (side)^

$= (\: 31) {}^{2} = \: 961cm {}^{2}$

$since \: 961cm { }^{2} > \: 880cm {}^{2}$

☘Hence, the square encloses more area.