Length of side

Question

a cube has a surface of 6x²+36x+54. Find the length of a side 

Answer 1

Hi Jamie,

 

In general, the surface area of a cube is the sum of the areas of all six faces.  Since each face is a square, the surface area S = 6s^2 since each face has an area of s^2 where s is the length of the side of the cube. 

 

If your cube has a surface area of 6x^2 + 36x + 54 and that surface area equals 6s^2, then

6s^2 = 6x^2 + 36x + 54

 

Notice that we can factor a 6 out of everything on the right side.  So we have

 

6s^2 = 6(x^2 + 6x + 9)

 

Dividing both sides by 6, we have

 

s^2 = x^2 + 6x + 9

 

The right side factors.

 

s^2 = (x + 3)^2

 

Take the square root of both sides and the the side length, s, is

 

s = x + 3

 

 

Hope this helps!  :)