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Setler [38]
3 years ago
10

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 cub

e and need to know how many square units of paint to purchase. If each face has side length s, then the formula S = 6s2 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 units2. What is the value of x? SHOW and EXPLAIN each of the steps you used to solve.
Mathematics
1 answer:
Ostrovityanka [42]3 years ago
6 0

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)**

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