Question 549374: What is the length of the edge of a cube if its volume could be doubled by an increase of 6 centimeters in one edge, an increase of 12 centimeters in a second edge, and a decrease of 4 centimeters in the third edge
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! What is the length of the edge of a cube if its volume could be doubled by an increase of 6 centimeters in one edge, an increase of 12 centimeters in a second edge, and a decrease of 4 centimeters in the third edge
:
Let x = the length of the cube featured here
then
x^3 = the volume of this cube
and
2x^3 = twice the volume
:
(x+6)*(x+12)*(x-4) = 2x^3
FOIL
(x^2 + 12x + 6x + 72)*(x-4) = 2x^3
(x^2 = 18x + 72)*(x-4) = 2x^3
Multiply
x^3 + 14x^2 - 288 = 2x^3
x^3 - 2x^3 + 14x^2 - 288 = 0
-x^3 + 14x^2 - 288 = 0
Just the sign of x^3 was changed, therefore we know that two of the factors of this equation: (x-6) and (x-12)
:
Check x=6 as the side of the original cube
Find the original volume 6^3 = 216 cu/units
Find the new volume:
(6+6)*(6+12)*(6-4) =
12 * 18 * 2 = 432 cu/units, twice the volume of 216
:
Do the same with x=12
Find the original volume 12^3 = 1728 cu/units
Find the new volume:
(12+6)*(12+12)*(12-4) =
18 * 24 * 8 = 3456 cu/units, twice the volume of 1728
:
we have two solutions for x, 6 and 12
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