9514 1404 393
Answer:
4 cm, 5 cm, 6 cm
Explanation:
If x represents the height of the original box, the other two dimensions are ...
width = x+1
length = x+2
and the volume is ...
V = HWL = x(x +1)(x +2) = x³ +3x² +2x
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After the change in dimensions, the height is 3x, the width is x+3, and the length is x+4. The new volume is ...
V = HWL = 3x(x+3)(x+4) = 3x³ +21x² +36x
The difference in volumes is ...
(3x³ +21x² +36x) -(x³ +3x² +2x) = 552
In standard form, this equation is ...
2x³ +18x² +34x -552 = 0
Factoring out 2 gives ...
x³ +9x² +17x -276 = 0
Possible rational roots are 1, 2, 3, 4, 6, and other divisors of 276. The largest possibility worth considering is less than ∛276 ≈ 6.5. Trial and error, or a graphing calculator can show us that x=4 is the only real solution to this equation.
The dimensions of the original small box are 4 cm × 5 cm × 6 cm.