Question

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?​

Answer 1

Question~

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?​ [Refer to the attachment given below]

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Given :

• Side of Square field = 60 m
• Length of Rectangle field = 80 m

To find :

• which field has a larger area

Solution :

• Here, the perimeter of the rectangular field is the same as the square field.

→ Perimeter of Rectangular field= Perimeter of Square Field

→ 2 (l + b) = 4 × s

→ 2 (80 + b) = 4 × 60

→ 160 + 2b = 240

→ 2b = 240 - 160

→ 2b = 80

→ b = 80/2

= 40 m

• Now, let's find the Area.

Area of Square = s × s

= 60 × 60

= 3600 m²

Area of Rectangle = l × b

= 80 × 40

= 3200 m²

Since,

= Area of Square ≥ Area of Rectangle

= 3600 m² ≥ 3200 m²

• The Area of Square has a larger area.