Question 1184667: 70 tiles each measure 3cm by 2cm.What is the area of the largest square possible using these tiles?
Answer by greenestamps(13200)   (Show Source):
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Each side of the square must have a length that is an integer multiple of both 2cm and 3cm, so the side of the square can be any integer multiple of 6x.
The area of the square is then (6x)^2 = 36x^2, where x is an integer.
The total area of the 70 tiles is 70(6)=420.
The area of the square can be...
x=1, area = 36(1^2)=36
x=2, area = 36(2^2)=144
x=3, area = 36(3^2)=324
x=4, area = 36(4^2)=576
ANSWER: The area of the largest square that can be made with the 70 tiles is 324 cm^2
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