Question

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

Answer 1

Answer:

Since, length of rectangle is 40 cm and breadth is 22cm.

Therefore, perimeter of the rectangle is :-

2×(length+breadth)

= 2×(40+22)

= 2× 62

= 124 cm is the perimeter.

Now, perimeter of rectangle= length of wire.

So, length of wire is 124 cm.

Now, if the same wire is in the shape of a square,

Then, the measure of each side= 124/4

= 31 cm.

Now, area of rectangle= l×b

= 40×22

= 880 cm²

And, area of square= side×side

= 31×31

= 961 cm²

Therefore, Square encloses more area.

Please mark brainliest.

Answer 2

$\purple \bigstar \large \tt Question$

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

Solution

Let consider a wire which is in the shape of rectangle now if this wire is bent in the shape of square so it must be obvious that the length of the wire wouldn't be altered at any cost this means that the Perimeter of rectangle = Perimeter of square .

➪ Perimeter of rectangle = 2 ( l + b )

We have ,

• Length ( l ) = 40 cm
• Breadth (b) = 22 cm

$\rm Perimeter \: of \: rectangle = 2(40 + 22) \\ = \tt 2 \times 62 = \colorbox{lime}{124 \: cm}$

Thus , Perimeter of Square will also be 124 cm.

We also know that,

$\sf \: Perimeter \: of \: Square = 4 \times side \\ \tt : \implies124 = 4 \times side \\ \rm \: \therefore side = \cancel\dfrac{124}{4} = \red{ 31cm}$

Therefore, each side of a square measures

31 cm.

Now , we have to find which of these two shapes enclosed more area .

1. Area of rectangle = Length × Breadth

$= 40 \times 22 = \tt \red{880 {cm}^{2}} \rightarrow(1)$

Now ,

• Area of Square = (side) ²

$= 31 \times 31 = \tt \red{961 {cm}^{2}} \rightarrow(2)$

On comparing, we can observe that square enclosed comparatively much area than rectangle.

Thankyou