SOLUTION: the dimension of rectangular metal box are 3cm 5cm and 8 cm. if the first 2 dimension are increased by the same numbers of centimeters, while the 3rd dimension remains the same, th

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Question 1187206: the dimension of rectangular metal box are 3cm 5cm and 8 cm. if the first 2 dimension are increased by the same numbers of centimeters, while the 3rd dimension remains the same, the new volume is 34cmcube more than the original volume. what is the new dimension of the enlarged rectangular metal box?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

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: 3.5 cm by 5.5 cm by 8 cm

Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
the dimension of rectangular metal box are 3cm 5cm and 8 cm.
if the first 2 dimension are increased by the same numbers of centimeters,
while the 3rd dimension remains the same, the new volume is 34cmcube more
than the original volume. what is the new dimension of the enlarged rectangular metal box?
~~~~~~~~~~~~~~ 

Let x be the linear increment.


Then you have this equation (write as you read the problem)

    (3+x)*(5+x)*8 - 3*5*8 = 34  cubic centimeters.


Make FOIL and simplify

    (15 + 8x + x^2)*8 - 120 = 34

     120 + 64x + 8x^2 - 120 = 34

     8x^2 + 64x - 34 = 0.


Find the roots using the quadratic formula and select the positive root, which is x = 0.5 cm.


ANSWER.  The new dimensions are  3.5 cm, 5.5 cm and 8 cm.

Solved.