Question

the perimeter of a rectangle and Square are same if the length and breadth of the rectangle are are 35 cm and 25 centimetre respectively find which figure has greater area and by how much​

Answer 1

Given Information :

• The perimeter of a rectangle and square are same.

• Length of the rectangle is 35 cm.

• Breadth of the rectangle is 25 cm.

To calculate :

• Which shape has more area and by how much?

Calculation :

In order to calculate which shape has more area and by how much, we need to calculate the area of both shapes first.

• Area of square = Side × Side
• Area of rectangle = Length × Breadth

Finding side of the square :

According to the question,

→ Perimeter of rectangle = Perimeter of square

• Perimeter of rectangle = 2 ( length + breadth )
• Perimeter of square = 4 × Side

→ 2 ( l + b ) = 4 × Side

→ 2 ( 35 cm + 25 cm ) = 4 × Side

→ 2 ( 60 cm ) = 4 × Side

→ 120 cm = 4 × Side

→ $\sf \dfrac {120}{4}$ cm = Side

→ 30 cm = Side

Therefore, side of the square is 30 cm.

$\large{\underline{\textsf{\textbf{ Area \:of \: square :}}}}$

→ Area of square = Side × Side

→ Area of square = 30 cm × 30 cm

→ Area of square = 900 cm²

$\large{\underline{\textsf{\textbf{ Area \:of \: rectangle :}}}}$

→ Area of rectangle = Length × Breadth

→ Area of rectangle = 35 cm × 25 cm

→ Area of rectangle = 875 cm²

Clearly,

● Area of square > Area of rectangle

Therefore, the square has greater area than the rectangle.

The difference of both's area will give the answer that by how much the area of square is greater than the area of rectangle.

→ Difference = (900 - 875) cm²

→ Difference = 25 cm²

Therefore, by 25 cm² the square has greater area than the rectangle.

Answer 2

Given :

• The perimeter of a rectangle and square are same.
• Length of Rectangle = 35cm
• Breadth of Rectangle = 25cm

To Find :

• Which figure has greater area and by how much.

Solution :

It was given that,

⟶⠀Square's peri. = Rectangle's peri.

⟶⠀4 × Side = 2(Length + Breadth)

⟶⠀4 × Side = 2(35 + 25)

⟶⠀4 × Side = 2 × 60

⟶⠀4 × Side = 120

⟶⠀Side = 120/4

⟶⠀Side = 30cm

Now,

⟶⠀Area of Square = (side)²

⟶⠀Area of Square = side × side

⟶⠀Area of Square = 30 × 30

⟶⠀Area of Square = 900cm²

And,

⟶⠀Area of Rectangle = Length × Breadth

⟶⠀Area of Rectangle = 35 × 25

⟶⠀Area of Rectangle = 875cm²

So,

✰ We can clearly see that Area of Square is bigger, so let's find by how much .

⟶⠀Area of Square - Area of Rectangle

⟶⠀900 - 875

⟶⠀25cm²

So, Area of Square is bigger than Area of Rectangle by 25cm²

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