The surface area of a cube is six times 𝑏 over two squared, where 𝑏 is a positive constant. Which of the following gives the perimeter of one face of the cube? A) two 𝑏, B) six 𝑏, C) 𝑏, or D) 𝑏 over two.
If we think about a cube, it’s made of six faces, all of which are squares. And if the surface area of a cube is six times 𝑏 over two squared, then 𝑏 over two squared is the area of each face of our cube, the area of a square. And we know that the area of a square equals side squared. And for us, 𝑏 over two squared is the area. 𝑏 over two squared equals side squared, where 𝑠 is the length of one of the sides of the square.
And we know that all four of the sides are the same length. If 𝑏 over two squared equals the area, then 𝑠, the side length, is just 𝑏 over two. And if one side measures 𝑏 over two, then the perimeter of our square is four times that side. The perimeter is four times 𝑏 over two. The four over two reduces to two. And we can say that the perimeter is two 𝑏. This makes sense because if we add 𝑏 over two plus 𝑏 over two, that would be equal to 𝑏.
The other two sides are also equal to 𝑏 over two. When we add those two sides together, we get 𝑏. And that means all four sides together would be two 𝑏, which is option A.