Answer: x equals 23
Step-by-step explanation: The information available to us is as follows;
Surface area of the cube = 1944
Side length of the cube = x - 5
Note however that the surface area is also derived as S = 6s²
In order to calculate the value of s we would start by substituting for the known values as follows;
S = 6s²
1944 = 6[(x - 5)²
1944 = 6[(x² - 10x + 25)]
By cross multiplication we now have
1944/6 = (x² - 10x + 25)
324 = x² - 10x + 25
Collect like terms and we now have;
x² - 10x -299 = 0
By factorization we now have;
(x - 23) (x + 13) = 0
Therefore, x - 23 = 0 and hence x = 23
OR
x + 13 = 0 and hence x = -13
Knowing that the length of the side is not a negative number, we would choose x = 23.
**(Having been given that x = 23,
s = x - 5
s = 23 - 5
s = 18)**
