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Q67 (CISF/2025) Science & Technology › Basic Science (Physics, Chemistry, Biology)

Two plots of land are equal in area. The first one is square shaped and the second one is circular. If p1 and p2 are the lengths of the boundaries of the square shaped plot and the circular plot respectively, then :

Explanation

Let the area of both plots be A.

For the square plot, Area = s2 = A, which gives side s = √A. The length of the boundary (perimeter) is p1 = 4s = 4√A.

For the circular plot, Area = πr2 = A, which gives radius r = √(A/π). The length of the boundary (circumference) is p2 = 2πr = 2π(√A/√π) = 2√π√A.

To compare p1 and p2, we compare the constants 4 and 2√π. Since π ≈ 3.14159, √π ≈ 1.772. Thus, 2√π ≈ 2 × 1.772 = 3.544.

Since 4 > 3.544, it follows that p1 > p2. Geometrically, this is explained by the isoperimetric inequality, which states that for a given area, the circle is the shape with the smallest possible perimeter.

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