Question

6. Awire is in the shape of a rectangle. Ils 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 rea?​

Answer 1

Step-by-step explanation:

According to the question,

Perimeter of square=Perimeter of rectangle

⇒4× side=2(length+breadth)

⇒4×side=2(40+22)

⇒4×side=2×62

⇒ side=

4

2×62

=31cm

Thus, the side of the square is 31cm.

Now, Area of rectangle=length×breadth=40×22=880cm

2

And Area of square=side×side=31×31=961cm

2

Therefore, on comparing, the area of square is greater than that of rectangle.

Answer 2

Answer:

• Each side of the square will be 31 cm
• Square will enclose more area.

Explanation:

Given

• Dimensions of a rectangle ( Awire enclosed with ) are 40 cm and 22 cm.

To Find

• The side of the square formes by rebending the same rectangle.
• The shape encloses more area.

Solution

Perimeter of a rectangle = 2 ( length + breath )

Perimeter = 2 ( 40cm + 22cm )

Perimeter = 2 ( 62cm )

Perimeter = 124cm

As we know, rectangle is rebent in a square, so their perimeter will be same.

Perimeter of the rectangle = Perimeter of the square

Perimeter of a square = 4 × side

Perimeter of the square = 124 cm

⟹ 4 × side = 124 cm

⟹ side = 124cm/4

⟹ side = 31 cm

Comparing Areas

Area of a rectangle = length × breath

Area = 22cm × 40cm

Area = 880 cm²

Area of a square = Side × side

Area = 31cm × 31cm

Area = 961 cm²

Square encloses more area