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Let the length, breadth and height of box be '3a', '2a' and 'a' cm respectively.
So, 3a X 2a X a = 546.75
Or, 6a 3 = 546.75
Or, a 3 = 91.125
Or, 'a' = 4.5
Length of box = 3 X 4.5 = 13.5 cm
Breadth of box = 2 X 4.5 = 9 cm
Height of box = 4.5 cm
Lateral surface area of box = 2 X (length + breadth) X height
= 2 X (13.5 + 9) X 4.5 = 9 X 22.5 = 202.5 cm 2
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