# SOLUTION: 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

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 Click here to see ALL problems on Geometry Word Problems 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 edgeAnswer by ankor@dixie-net.com(15652)   (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