A big rectangular plot of area 4320 Sq.m is divided into 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 plot 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 a surplus. What are the dimensions of the original plot?

Areas 26/09/2020

A. 160m × 27m
B. 240m × 18m
C. 120m × 36m
D. 135m × 32m

Let the side of smaller square at the extreme right be a

Then side of the larger square is 3a
Total area of the field = a2 + a2 +a2 + (3a)2 +(3a)2 = 30a2
Therefore, 30 a2 = 4320 => a2 = 432 / 3 = 144 => a = 12
Smaller side of the field = 36
Larger side of the field = (3a) × 3 + a = 10 a = 10 × 12 = 120
Original Dimensions of the field = 120m × 36m

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