Question

the perimeter of a rectangle and square are seemed the length and breadth of the rectangle are 50 cm and 34 CM respectively find which future has greater area and by how much​

Answer 1

Given :

• The perimeter of a rectangle and square are same.

• Length of Rectangle = 50cm

• Breadth of Rectangle = 34cm

To find :

• Find which figure has greater area and by how much.

Solution :

• In the question it is given That perimeter of Rectangle and square are same. So, Firstly we will find the side of the square By using Perimeter of Rectangle = Perimeter of square 2 (L + B) = 4 × Side. Then, we will get the required Side of the Square.

• Then, we need to find which figure has greater area and by how much. We will find the Area of rectangle and square And then we will get which figure has the greatest area.

Perimeter of rectangle = Perimeter of square

→ 2 (L + B) = 4 × Side

→ 2 (50 + 34) = 4 × side

→ 2 × 84 = 4 × side

→ 168 = 4 × side

→ side = 168/4

→ side = 42.

Area of Rectangle = L × B

→ 50 × 34

→ 1700cm²

Area of Square = (side)²

→ (42)²

→ 1764cm²

1764 - 1700 = 64

∴ The area of square Is greater than area of rectangle By 64 cm.

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Answer 2

Given :

• The perimeter of a rectangle and square are same.
• Length of Rectangle = 50cm
• Breadth of Rectangle = 34cm

To Find :

• Which figure has greater area and by how much.

Solution :

✰ In this question, it is given that the perimeter of a rectangle and square are same and length and breadth of the rectangle are 50cm and 34cm respectively and we have to find which figure has greater area and by how much. Now, firstly we will find the side of the square after that we will find the Area of Square and Area of Rectangle separately . After getting the both the Areas, we will substract the smaller area from the bigger area to find whose area is bigger.

⠀

⠀⠀⟼⠀⠀Both have same perimeter

⠀⠀⟼⠀⠀4 × side = 2(Length + Breadth)

⠀⠀⟼⠀⠀4 × side = 2(50 + 34)

⠀⠀⟼⠀⠀4 × side = 2 × 84

⠀⠀⟼⠀⠀side = 2 × 84/4

⠀⠀⟼⠀⠀side = 168/4

⠀⠀⟼⠀⠀side = 42cm

⠀

Thus Side of Square is 42cm

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Area of Rectangle :

• Area = Length × Breadth
• Area = 50 × 34
• Area = 1700cm²

Thus Area of Rectangle is 1700cm²

___________________

Area of Square :

• Area = (side)²
• Area = side × side
• Area = 42 × 42
• Area = 1764cm²

Thus Area of Square is 1764cm²

___________________

Finding the Difference :

• Area of Square - Area of Rectangle
• 1764 - 1700
• 64cm

Therefore, Area of Square is bigger then Area of Rectangle by 64cm

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