Answer:

Let's denote the width of the rectangular tank as x. Then, the length would be 3x, and the height would be 2 + 2x.

The formula for the volume of a rectangular tank is:

Volume = Length x Width x Height

Substituting the values we have:

216 = (3x)(x)(2+2x)

Expanding the equation and simplifying, we get:

3x^3 + 3x^2 - 108 = 0

Factoring out 3, we get:

3(x^3 + x^2 - 36) = 0

Solving for x using either factoring or the quadratic formula, we get:

x = 3 or x = -4.78 (approximately)

Since the width of the tank cannot be negative, the width must be 3 units. Substituting this value back into the original equations, we get:

Length = 3(3) = 9 units

Height = 2 + 2(3) = 8 units

Therefore, the dimensions of the tank are 9 units in length, 3 units in width, and 8 units in height

Answer:

l = 3w (the length is 3 times the width)

h = 2w + 2 (the height is 2 more than twice the width)

lwh = 216 (the volume is 216 cubic units)

l = 216 / (wh)

Substituting the expressions we have for l, h, and w in terms of each other:

3w = l

2w + 2 = h

w(3w)(2w + 2) = 216

We can simplify the third equation by distributing the w:

6w^3 + 6w^2 = 216

Dividing both sides by 6:

w^3 + w^2 - 36 = 0

Now, we can solve for w using factoring:

w^3 + w^2 - 36 = (w - 3)(w + 4)(w + 3) = 0

So, the dimensions of the tank are width = 3 units, length = 9 units, and height = 8 units.

Step-by-step explanation: