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 where the dimensions of the original cube?

Answer:The dimensions of the original cube are 16 in x 16 in x 16 inStep-by-step explanation:Letx ----> the length side of the original cubeThe surface area of the cube is equal to[tex]SA=6b^2[/tex]whereb is the length side of the cubewe know thatThe dimensions of a cube are reduced by 4 inches on each side and the surface area of the new cube is 864 square inchessoThe length side of the new cube is[tex]b=(x-4)\ in[/tex]substitute in the formula of surface area[tex]SA=6(x-4)^2[/tex][tex]SA=864\ in^2[/tex]so[tex]6(x-4)^2=864[/tex]Simplify[tex](x-4)^2=144[/tex]take square root both sides[tex](x-4)=(+/-)12[/tex][tex]x=4(+/-)12[/tex][tex]x=4(+)12=16\ in[/tex][tex]x=4(-)12=-8\ in[/tex] ----> the length side cannot be a negative numberthereforeThe dimensions of the original cube are 16 in x 16 in x 16 in