Question

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 ?

Answer 1

Answer:

14 times Tia's share of land is equal to 11 times Virom's share of land.

Step-by-step explanation:

Bennett bhai, I don't know how to generalize it but I came to this conclusion by putting square's side as 7. By making their perimeters(and circumference) equal, radius came to be 14/pi. Take circle's area; it will come out to be 62.3 and square's area will be 49.

62.3*11 = 685.3

49*14 = 686

They both are approximately equal; thus the conclusion : 14 times Tia's share of land is equal to 11 times Virom's share of land.

Answer 2

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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