Answer:
x = 6 cm
Explanation:
Volume of a rectangular prism = length × width × height
Length = 5 cm
Width = (x + 12) cm
Height = (x + 6) cm
Volume of a rectangular prism = 1,080 cubic centimeter
Volume of a rectangular prism = length × width × height
1080 = 5 * (x+12) * (x+6)
1080 = 5 (x^2 + 6x + 12x + 72
1080 = 5 (x^2 + 18x + 72)
1080 = 5x^2 + 90x + 360
Divide through by 5
216 = x^2 + 18x + 72
Subtract 216 from both sides
x^2 + 18x + 72 - 216= 0
x^2 + 18x - 144 = 0
Using factorization method to solve the quadratic equation
x^2 + 24x - 6x - 144 = 0
x( x+ 24) - 6 ( x + 24) = 0
(x + 24) (x - 6) = 0
x + 24 = 0
x = -24
x - 6 = 0
x = 6
x = -24 or 6
x can not be a negative value , so, x = 6 cm