Question

1. The area of a square park is same as of a rectangular park. If the side of the square park is 80 m and the length of the rectangular park is 100 m, find the breadth of the rectangular park. Which figure encloses more perimeter​.

Answer 1

Given :-

• The area of a square park is same as of a rectangular park
• Side of Square park = 80m
• Length of Rectangular park = 100m

To Find :-

• Breadth of the Rectangle
• Figure that encloses more perimeter

Solution :-

❏ It is given that, The area of a square park is same as of a rectangular park , therefore :

➞ Area of Square = Area of Rectangle

➞ (side)² = Length × Breadth

➞ side × side = Length × Breadth

➞ 80 × 80 = 100 × Breadth

➞ 6400 = 100 × Breadth

➞ 6400 / 100 = Breadth

➞ 64m = Breadth

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⟾ Perimeter of Square = 4 × Side

⟾ Perimeter of Square = 4 × 80

⟾ Perimeter of Square = 320m

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➟ Perimeter of Rectangle = 2 ( L + B )

➟ Perimeter of Rectangle = 2 (100 + 64)

➟ Perimeter of Rectangle = 2 × 164

➟ Perimeter of Rectangle = 328m

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Therefore :

• Breadth of Rectangle = 64m
• Rectangle encloses more perimeter.

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★ Additional Info :

Formulas Related to Rectangle :

• Perimeter of Rectangle = 2( l + b)
• Area = Length × Breadth
• Length = Area / Breadth
• Breadth = Area / Length
• Diagonal = √(l)² + (b)²

Formulas Related to Square :

• Perimeter = 4 × Side
• Area = Side × Side
• Side of Square = √Area
• Diagonal = √2 × Side
• Area = ½ × (Diagonal)²
• Area = (Perimeter ÷ 4)²

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