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

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#### Solution

Perimeter of square = 4 (Side of the square) = 4 (60 m) = 240 m

Perimeter of rectangle = 2 (Length + Breadth)

= 2 (80 m + Breadth)

= 160 m + 2 × Breadth

It is given that the perimeter of the square and the rectangle are the same.

160 m + 2 × Breadth = 240 m

Breadth of the rectangle = `(80/2)m `= 40 m

Area of square = (Side)^{2} = (60 m)^{2} = 3600 m^{2}

Area of rectangle = Length × Breadth = (80 × 40) m^{2} = 3200 m^{2}

Thus, the area of the square field is larger than the area of the rectangular field.

Concept: Mensuration

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