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Question
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 m2
Area of rectangle = Length × Breadth = (80 × 40) m2 = 3200 m2
Thus, the area of the square field is larger than the area of the rectangular field.
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