Answer:
To find the dimensions of the fish tank, we can set up the equation:
(width) * (length) * (height) = 1440 cubic inches
Substituting the given expressions for the dimensions of the tank, we get:
(w) * (w + 8) * (18 - w) = 1440
This is a quadratic equation in w, and we can solve it using the quadratic formula:
w = (-(w + 8) +/- sqrt((w + 8)^2 - 4*(18 - w)11440)) / (2*1)
This simplifies to:
w = (-(w + 8) +/- sqrt(w^2 + 16w + 64 - 72w + 5760)) / 2
= (-(w + 8) +/- sqrt(w^2 - 56w + 5760)) / 2
We can further simplify this equation by factoring:
w = (-(w + 8) +/- sqrt((w - 40)(w - 144))) / 2
We can then solve for w by setting each factor equal to zero:
w - 40 = 0 => w = 40
w - 144 = 0 => w = 144
Since the width of the fish tank must be greater than 6 inches, the only valid solution for w is 40 inches. Substituting this value back into the equation for the volume of the tank, we find that the length of the tank is 48 inches (w + 8 = 40 + 8 = 48) and the height of the tank is 12 inches (18 - w = 18 - 40 = 12).
Therefore, the dimensions of the fish tank are:
width: 40 inches
length: 48 inches
height: 12 inches
The correct answer is therefore (a) width: 12 in., length: 20 in., height: 6 in.
Explanation: