Question

14. A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the
same wire is re-bent in the shape of a square, what will be the measure of each side?
Also, find which shape encloses more area?
​

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.

How satisfied are you with the

Answer 2

Given :

Length and Breadth of a rectangle are 40 cm and 22 cm .

To Find :

• Measure of Each Side of Square .

• Shape which encloses more area .

Solution :

Length of a Rectangular Wire = 40cm

Breadth of a Rectangular Wire = 22cm

Formula Used :

$\bigstar\:\sf{Perimeter\:of\: Rectangle=2(l+b)}$

2 (40 + 22)

2 (62)

124 cm

So , The Perimeter of Rectangle is 124cm .

So :

Perimeter of Square = Perimeter of Rectangle

4 × Side = 124

Side = 124/4

Side = 31 cm

So , The Side of the Square is 31 cm .

____________________________

Formula Used :

$\bigstar\:\sf{Area\:of\: Rectangle=Length\times{breadth}}$

40 × 22

880 cm²

Formula Used :

$\bigstar\:\sf{Area\:of\: Square={Side}^{2}}$

31 × 31

961 cm²

So , Square encloses more area .