Answer:
x = 23
Step-by-step explanation:
We know that the surface area of a cube is denoted by S = 6s². In this case, we see that s = x - 5, so just plug x - 5 in for s in the formula:
S = 6(x - 5)²
We also know that the surface area is 1944, so S = 1944. Plug this in as well:
S = 6(x - 5)²
1944 = 6(x - 5)²
Now, we solve by expanding the right:
1944 = 6(x² - 10x + 25) = 6x² - 60x + 150
Subtract 1944 from both sides:
6x² - 60x - 1794 = 0
Divide by 6 from both sides for simplicity:
x² - 10x - 299 = 0
Factor:
(x - 23)(x + 13) = 0
x = 23 or x = -13
Obviously, we can't have a negative length, so -13 is wrong. We use x = 23 instead.
The answer is thus x = 23.
