Question

a square and a rectangular field with measurements are given in the figure have the same perimeter which field has a larger area ¿?​

Answer 1

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Perimeter of Square = 4 x side = 4 x 60 = 240 sq metres

Perimeter of Square = 4 x side = 4 x 60 = 240 sq metresArea of Square = Side² = 60² = 3600 square metre

Perimeter of Square = 4 x side = 4 x 60 = 240 sq metresArea of Square = Side² = 60² = 3600 square metrePerimeter of Rectangle = 2(length + breadth)

Perimeter of Square = 4 x side = 4 x 60 = 240 sq metresArea of Square = Side² = 60² = 3600 square metrePerimeter of Rectangle = 2(length + breadth) 240 = 2(80 + breadth)

Perimeter of Square = 4 x side = 4 x 60 = 240 sq metresArea of Square = Side² = 60² = 3600 square metrePerimeter of Rectangle = 2(length + breadth) 240 = 2(80 + breadth) 80 + breadth = 120

Perimeter of Square = 4 x side = 4 x 60 = 240 sq metresArea of Square = Side² = 60² = 3600 square metrePerimeter of Rectangle = 2(length + breadth) 240 = 2(80 + breadth) 80 + breadth = 120 breadth = 120-80 = 40 metres

Perimeter of Square = 4 x side = 4 x 60 = 240 sq metresArea of Square = Side² = 60² = 3600 square metrePerimeter of Rectangle = 2(length + breadth) 240 = 2(80 + breadth) 80 + breadth = 120 breadth = 120-80 = 40 metresArea of rectangle = length x breadth = 80 x 40 = 3200 square metres

Perimeter of Square = 4 x side = 4 x 60 = 240 sq metresArea of Square = Side² = 60² = 3600 square metrePerimeter of Rectangle = 2(length + breadth) 240 = 2(80 + breadth) 80 + breadth = 120 breadth = 120-80 = 40 metresArea of rectangle = length x breadth = 80 x 40 = 3200 square metresNow it is clear that the area of the square field is greater than the area of the rectangular field.

Answer 2

Step-by-step explanation:

Side of a square = 60 m (Given)

And the length of rectangular field, l = 80 m (Given)

According to question,

Perimeter of rectangular field = Perimeter of square field

2(l+b) = 4×Side (using formulas)

2(80+b) = 4×60

160+2b = 240

b = 40

Breadth of the rectangle is 40 m.

Now, Area of Square field

= (side)2

= (60)2 = 3600 m2

And Area of Rectangular field

= length×breadth = 80×40

= 3200 m2

Hence, area of square field is larger.