Question

pls answer question 6​

Answer 1

Given :-

A wire is in the shape of a rectangle .

Length = 40 cm

Breadth = 22cm

Required to find :-

• Measurement of side of the square ?

• Which shape encloses more area ?

Formulae used :-

$\Large{\dagger{\boxed{\sf{ Perimeter \; of \; a \; rectangle = 2 ( length + breadth ) }}}}$

$\Large{\dagger{\boxed{\sf{Perimeter \; of \; a \; square = Side \times 4 }}}}$

$\Large{\dagger{\boxed{\sf{Area \; of \; a \; rectangle = length \times breadth }}}}$

$\large{\dagger{\boxed{\rm{Area \; of \; a \; square = Side \times Side }}}}$

SoLuTioN :-

Given :-

A wire is in the shape of a rectangle .

Length = 40 cm

Breadth = 22cm

So,

Using the formula,

$\Large{\dagger{\boxed{\sf{ Perimeter \; of \; a \; rectangle = 2 ( length + breadth ) }}}}$

Hence,

Perimeter of a rectangle = 2 ( 40 + 22 )

Perimeter of the rectangle = 2 ( 62 )

Perimeter of the rectangle = 124 cm

Similarly,

It is also mentioned that ;

The wire was re-bent to form a square

So, we can conclude that :-

• Perimeter of the rectangle = Perimeter of the square

So,

Perimeter of the square = 124 cm

But,

Let the side be " x " cm

Using the formula,

$\Large{\dagger{\boxed{\sf{Perimeter \; of \; a \; square = Side \times 4 }}}}$

$\tt{ 124 = x \times 4 }$

$\tt{ 124 = 4x }$

$\tt{ 4x = 124 }$

$\tt{ x = \dfrac{124}{4} }$

$\tt{ x = 31 }$

Hence,

• Side of the square = 31 cm

Now we need to find the area enclosed by these shapes

Area enclosed by rectangle is ;

Dimensions :-

Length = 40 cm

Breadth = 22 cm

Using the formula ,

$\Large{\dagger{\boxed{\sf{Area \; of \; a \; rectangle = length \times breadth }}}}$

So,

Area of the rectangle = 40 x 22

Area of the rectangle = 880 m²

Similarly,

Area enclosed by square is ;

Dimensions ;

Side = 31 cm

Using the formula,

$\large{\dagger{\boxed{\rm{Area \; of \; a \; square = Side \times Side }}}}$

So,

Area of a square = 31 x 31

Area of a square = 961 m²

By comparison of both areas enclosed by the shape

We can conclude that ,

The square encloses more area when compared to rectangle

The difference between the areas enclosed is ;

=> 961 - 880

=> 81 m²

Answer 2

Qᴜᴇsᴛɪᴏɴ:-

A wire is in the shape of a rectangle. It's 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?

Fᴏʀᴍᴜʟᴀs Usᴇᴅ:-

Perimeter of a rectangle = 2 * (length + breadth)

Perimeter of a square = 4 * side

Area of a rectangle = length * breadth

Area of a square = side * side

Aɴsᴡᴇʀ:-

First we have to find total length of wire:-

Total length of wire = Perimeter of rectangle = 2 * (length + breadth)

=> 2 * (40 + 22) cm

=> 2 * 62 cm

=> 124 cm

Wire is rebent to form a square:-

Total perimeter of square = Total length of wire

=> 4 * side = 124 cm

=> side = 124/4 cm

=> side = 31 cm

Therefore, length of each side of square = 31 cm.

Area of rectangle:-

Area = length * breadth

=> Area = 40 cm * 22 cm

=> Area = 880 cm²

Area of square:-

Area = side * side

=> Area = 31 cm * 31 cm

=> Area = 961 cm²

880 cm² < 961 cm²

Area of rectangle < Area of square

Area of square - Area of rectangle = 961 cm² - 880 cm² = 81 cm²

Therefore, area of square is more than area of rectangle by 81cm²

Answer:- 1) 31 cm

2) Area of square is more than area of rectangle by 81cm²