Question

The surface area of a cube is 6(a/4)^2, where a is a positive constant. What is the perimeter of one face of the cube?

Answer 1

Answer: The perimeter is $a$

Step-by-step explanation:

1. By definition, the formula for calculate the surface area of a cube is:

$SA=6s^{2}$

Where s is the lenght of any edge of the cube.

2. You know that the surface area of the cube of the problem is $6(a/4)^{2}$, therefore the lenght of each edge of the cube is:

$s=a/4$

3. Each face of the cube is a square, therefore the perimeter of one face is:

$P=4s$

$P=4(a/4)$

$P=4a/4$

$P=a$