Answer:
 4 cm
Step-by-step explanation:
After the cut of length x from each corner, the size of the base will be ...
 (30 -2x) by (60 -2x)
You want to find x such that the product of these dimensions is 1144.
 (30 -2x)(60 -2x) = 1144
 (15 -x)(30 -x) = 286 . . . . . . divide by 4
 x^2 -45x +450 = 286 . . . . eliminate parentheses
 x^2 -45x +164 = 0 . . . . . . . subtract 286
 (x -4)(x -41) = 0 . . . . . . . . . . factor
The solution that is less than 15 cm is x = 4.
The sides of the squares are 4 cm.
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