Shreya buys two plots of land. The 1st plot is a square and the 2nd one is a
circle. She buys wires to make a boundary for both the plots and observes
that it took same length of wire to make the boundary for each plot.
Believing that she is being fare and equal in her distribution, Shreya gifts
the square plot to her daughter, Tia and the circular plot to her son, Virom.
Which of the following statement describes Shreya's decision, most
appropriately?
Answers
Given : Shreya buys two plots of land. The 1st plot is a square and the 2nd one is a circle. She buys wires to make a boundary for both the plots and observes that it took same length of wire to make the boundary for each plot.
To Find : Relation in Area of plots
Solution:
Let say wire Length = 4X unit
Perimeter of Square = 4 * Side
=> 4 * Side = 4X
Hence side of Square plot = X unit
Area of Square plot = X² sq unit
Perimeter of Circle = 2πR
2πR = 4X
=> R = 2X/π
Area of circular Plot = πR²
= π (2X/π)²
= 4X²/π
Area of Square plot = X² sq unit
Area of circular Plot = (4/π) X² sq unit
4/π = 4/(22/7) = 14/11
Area of Square plot = X² sq unit
Area of circular Plot = (14/11) X² sq unit
=> 14 x Area of Square plot = 11 x Area of circular Plot
=> Area of Square plot / Area of circular Plot = 11/14
Area of circular Plot is more than Square plot
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