Question 1187206
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x = amount we increase the first two dimensions by
The x is a placeholder for some positive number
The old box is 3 by 5 by 8
The new box is (3+x) by (5+x) by 8


The old volume was
V1 = 3*5*8 = 120 cm^3


The new volume is
V2 = (3+x)*(5+x)*8
V2 = (15+3x+5x+x^2)*8
V2 = 8(x^2+8x+15)
V2 = 8x^2+64x+120


This new volume (V2) is 34 cm^3 larger compared to the old volume (V1)


V2 = V1 + 34
8x^2+64x+120 = 120 + 34
8x^2+64x+120 = 154
8x^2+64x+120-154 = 0
8x^2+64x-34 = 0
2(4x^2+32x-17) = 0
4x^2+32x-17 = 0


Use factoring or the quadratic formula to find the two possible solutions are:
x = -17/2 or x = 1/2
Ignore the first solution. Negative lengths are not possible.


The only practical solution is that we increased the first two dimensions by 1/2 = 0.5 cm


The first two dimensions of 3 cm and 5 cm become 3.5 cm and 5.5 cm


Old Box = 3 cm by 5 cm by 8 cm
New Box = 3.5 cm by 5.5 cm by 8 cm
Old volume = 3*5*8 = 120
New volume = 3.5*5.5*8 = 154
Difference in volumes = 154-120 = 34
The answer is confirmed.


Answer: <font color=red>3.5 cm by 5.5 cm by 8 cm</font>
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