Question

to playground have the same perimeter one is rectangular in shape it is 40 m long and 25 m and either square which one is the largest in the area and by how much​

Answer 1

Given that,

• The Length and Breadth of Rectangle are 40m and 25m respectively.
• The Perimeter of Rectangle and Square is same.

To Find,

• Which one is the largest in the area and By how much?

Solution,

Finding the Perimeter of Rectangle,

As we know,

• Perimeter of Rectangle = 2( l + b )

We found,

• •➤ Perimeter = 2(40 + 25)m
• •➤ Perimeter = 2(65)m
• •➤ Perimeter = 130m

Hence, The Perimeter of Rectangle is 130m.

Finding the Length of Side of Square,

As given,

• The Perimeter of Square = The Perimeter of Rectangle

As we know,

• The Perimeter of Square = 4 × a

We found,

• •➤ 4 × a = 130m
• •➤ a = 32.5m

Hence, The Length of Side of Square is 32.5m.

Finding the Area of Both Polygons,

As we know,

• The Area of Rectangle = l × b

We found,

• •➤ Area = 40 × 25 m²
• •➤ Area = 1000m²

Hence, The Area of Rectangle is 1000m².

As we know,

• The Area of Square = a × a

We found,

• •➤ Area = 32.5 × 32.5 m²
• •➤ Area = 1056.25m²

Hence, The Area of Square is 1056.25m².

Therefore,

• The Area of Square is greater than the Area of Rectangle by 56.25m² [1056.25 - 1000 = 56.25].

Required Answer,

• The Area of Square is greater than the Area of Rectangle by 56.25m².