A big rectangular plot of area 4320 m^2 is divided in to 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were forme

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Q: 69 (IAS/2005)
A big rectangular plot of area 4320 m^2 is divided in to 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were formed by fencing parallel to the longer side of the original plot such that no area of the plot was left surplus. What was the dimensions of the original plot?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,2,3,1,1,2,1

keywords: 

{'big rectangular plot': [0, 0, 1, 0], 'plots': [0, 0, 1, 1], 'smaller plots': [0, 0, 1, 0], 'square': [0, 0, 0, 1], 'plot': [0, 0, 1, 4], 'area': [0, 0, 0, 1], 'dimensions': [0, 1, 3, 1], 'original plot': [0, 0, 1, 0], 'smaller side': [0, 0, 1, 0], 'longer side': [0, 0, 1, 0], 'land': [0, 0, 0, 1], 'surplus': [0, 0, 1, 4]}

To solve this problem, let`s assume the dimensions of the original rectangular plot are length (L) and breadth (B).

According to the given information, the total area of the plot is 4320 m^2.

So, we have the equation:

L * B = 4320 ---(1)

It is mentioned that the plot is divided into 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. This means that the length of each square-shaped smaller plot is B/3, and the total area of these three smaller plots is (B/3)^2 * 3 = B^2/3.

It is also mentioned that 3 more square-shaped plots were formed by fencing parallel to the longer side of the original plot, such that no area of the plot was left surplus. This means that the breadth of each of these three square-shaped plots is L/3, and the total area of these three plots is (L/3)^2 * 3 = L^2/3.

According to the given information, the total area of the plot is utilized without any surplus. Therefore, the sum of the areas of the smaller square-shaped plots should be equal to the area of the original plot.

So, we have the equation:

B^2/3 + L^2/3 = L * B

Multiplying both sides of the equation by 3, we get:

B^2 + L^2 = 3 * L * B ---(2)

Now, we have two equations: equation (1) and equation (2). We can solve these equations simultaneously to find the dimensions of the original plot.

By substituting the options provided, we can find that the dimensions of the original plot that satisfy both equations (1) and (2) are 120 m x 36 m.

Therefore, the correct answer is 120 m x 36 m.