Final answer:
To find the area of the base, substitute the expression x+4 into the given equation and expand. The value of the area of the base is 64.
Step-by-step explanation:
To find the area of the base, we need to determine the value of the expression x+4 when given the height. Since height is represented by x+4, we substitute this expression into the original equation:
x³+12x²+47x+60 = (x+4)³
We can now expand the right side of the equation using the binomial cube formula:
(x+4)³ = x³ + 3x²(4) + 3x(4)² + 4³ = x³ + 12x² + 48x + 64
Comparing this expanded form to the original equation, we can see that the values of the expressions x+4 and x³+12x²+48x+64 are equal.
Therefore, the value of the area of the base is 64.