For this case we have the following equation for the volume:
\(x ^ 3 + 6x ^ 2-27x = 140
\)
Rewriting the equation we have:
\(x ^ 3 + 6x ^ 2-27x-140 = 0
\)
We factor the equation to find the roots of the polynomial.
We have then:
\((x-5) (x + 4) (x + 7) = 0
\)
Then, we discard the negative roots, because the dimensions of the figure must be positive.
We have then that the length is:
\(x = 5
\)
The height is:
\(x + 9 = 5 + 9 = 14
\)
The width is:
\(x-3 = 5-3 = 2
\)
Thus, the dimensions are:
\(5 * 14 * 2
\)
Answer:
The length is 5 inches, the width is 2 inches, and the height is 14 inches.
