Question

The perimeter of a rectangle and square are same. If the length and breadth of the rectangle are 25 cm and 17 cm respectively, which figure has greater area and how much?

Answer 1

Answer:

perimeter of a rectangle = perimeter of square

2 ( l+ b ) = 4 × side

2 ( 25 + 17 ) = 4 × side

2 × 42 = 4× side

84 = 4 × side

84 / 4 = side

21 = side of square

area of square = (side)^2

= 21 × 21

= 441 cm^2

area of rectangle = length × breadth

= 25 × 17

= 425 cm

hence you can see that 441 cm^2 is greater than 425 cm which means area of sqauare is greater than area of rectangle

Answer 2

• Given

• Perimeter of rectangle and square are equal.
• Length of rectangle = 25 cm
• Breadth of rectangle = 17 cm

• To find

• Which figure has greater are and by how much

• How to solve?

• The length and breadth of rectangle of rectangle are given. Firstly, we will find the are of rectangle.
• As mentioned in he question, Perimeter if rectangle = Perimeter of square.
• So, we will find the perimeter if rectangle and then from it we will find the side of square.
• Using the side we will find the area of square.
• Now compare both the areas and we're done.

Formulae to be used

• Perimeter of rectangle = 2(l + b)
• Area of rectangle = length × breadth
• Perimeter if square = 4 × side
• Area of square = side²

• Solution

• Area of rectangle

⇒ 25 × 17

⇒ 425 cm²

• Area of rectangle = 425 cm²

• Perimeter of rectangle = 2(l + b)

⇒ 2(25 + 17)

⇒ 2(42)

⇒ 84 cm

• Perimeter of rectangle = 84 cm

Perimeter of rectangle = Perimeter of square

• Perimeter of square = 4 × side

⇒ 84 = 4 × side

⇒ 84/4 = side

⇒ 21 = side

• Side of square = 21 cm each

• Area of square = side²

⇒ (21)²

⇒ 441 cm²

• Area of square = 441 cm²

Area of rectangle = 425 cm²

Area of square = 441 cm²

The figure with greater area is square.

⇒ (441 - 425) cm²

⇒ 16 cm²

•°• Area of square is greater than area of rectangle by 16 cm².