A rectangular prism has a volume of 3x2 + 18x + 24. Its base has a length of x + 2 and a width of 3. Which expression represents the height of the prism?
1) x + 4
2) x + 2
4) x2 + 6x + 8
The volume of any prism can also be given as the base area of that prism multiplied by the height. That is,
Volume of prism = Area of base x Height of prism
for a rectangular base,
Area of base = Length x Width.
Thus, volume of the rectangular prism = Length x Width x Height
3x2 + 18x + 24 = (x + 2) * 3 * h
divide through by 3
x2 + 6x + 8 = (x + 2)h
Divid both sides by x+2
h = (x2 + 6x + 8) / (x + 2)
from division of polynomial, h = x + 4