SOLUTION: When the dimensions of a cube are reduced by 4 inches on each side, the surface area of the new cube is 864 square inches. What were the dimensions of the original cube?

Algebra ->  Surface-area -> SOLUTION: When the dimensions of a cube are reduced by 4 inches on each side, the surface area of the new cube is 864 square inches. What were the dimensions of the original cube?      Log On


   

Question 371640: When the dimensions of a cube are reduced by 4 inches on each side, the surface area of the new cube is 864 square inches. What were the dimensions of the original cube?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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When the dimensions of a cube are reduced by 4 inches on each side,
the surface area of the new cube is 864 square inches.
What were the dimensions of the original cube?
:
Let x = length of sides in the original cube
:
Surface area of original cube = 6x^2
:
New cube surface area:
6(x-4)^2 = 864
:
FOIL (x-4)(x-4)
6(x^2 - 8x + 16) = 864
:
Divide both sides by 6
x^2 - 8x + 16 = 144
:
A quadratic equation
x^2 - 8x + 16 - 144 = 0
x^2 - 8x - 128 = 0
:
Factors to:
(x-16)(x+8) = 0
:
positive solution:
x = 16 inches, side of original cube
:
:
New cube side will be 12 inches, find the surface area of new cube:
6(12^2) = 864, confirms our solution