Question

!DUE TODAY, PLEASE HELP!

The surface area S of a cube is equal to the sum of the areas of the 6 square faces that form the cube. We want to paint the cube and need to know how many square units of paint to purchase. If each face has side length s, the the formula s=6s^2 can be used to find the surface area of the cube. The length of a side is indicated in the cube below (s=x-5). The surface area of the cube is 1944 units^2.

What is the value of x? SHOW and EXPLAIN each step you used to solve.

Answer 1

x = 23

Explanation:

surface area of a cube = 6s²

Side length, s = x - 5

Surface area of the cube = 1944 units²

What is the value of x?

surface area of a cube = 6s²

1944 = 6(x - 5)²

1944/6 = (x - 5)²

324 = (x - 5)²

324 = x² - 10x + 25

x² - 10x + 25 - 324 = 0

x² - 10x - 299 = 0

Solve quadratic equation using factorization

(x + 13) (x - 23) = 0

x + 13 = 0 or x - 23 = 0

x = -13 or x = 23

The side length can not be negative

Therefore, x = 23