The surface area of a cube is6( 4a​ ) 2 , whereais a positive constant. Which of the following gives the perimeter of one face of the cube?

The surface area of a cube is given by the formula 6s^2, where s is the length of one side of the cube. In this case, the surface area is given as 6(4a)^2.

Step 1: Set the two expressions for the surface area equal to each other:

6s^2 = 6(4a)^2

Step 2: Simplify the right side of the equation:

6s^2 = 6*16a^2

Step 3: Divide both sides by 6:

s^2 = 16a^2

Step 4: Take the square root of both sides to solve for s:

s = 4a

The perimeter of one face of the cube (which is a square) is given by the formula 4s. Substituting 4a for s gives the perimeter as 4(4a) = 16a.

So, the perimeter of one face of the cube is 16a.