By definition we have that the volume is given by:
\(V=(w)*(l)*(h)\)
Where,
w: with
l: length
h: height
Substituting values we have:
\(7.6 = (x) * (x + 5) * (3x-1)\)
Rewriting:
\(7.6 = 3x ^ 3 + 14x ^ 2 - 5x\)
We look for the roots of the polynomial:
\(x1 = -4.9
x2 = -0.6
x3 = 0.85\)
We discard the negative roots because we want to find dimensions.
Thus, the dimensions are:
\(w = 0.85 feet = 10.2 inches
l = 5.85 feet = 70.2 inches
h = 1.55 feet = 18.6 inches\)
Answer:
the dimensions in inches are:
w = 10.2 inches
l = 70.2 inches
h = 18.6 inches
