The dimensions, in inches, of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x - 1. The volume is about 7.6 ft3. Find the dimensions of the box in inches.

Answer 1

To solve for the dimensions, we need to first express the volume in inches.
There are 12 inches in 1 foot, so 7.6 ft^3 is equal to 7.6 x 12^3 = 7.6 x 1728 = 13107.2 in^3.
The volume of a rectangular box is given by length x width x height.
So, (x)(x + 5)(3x - 1) = 13107.2.
Expanding the expression, we get: 3x^3 + 14x^2 - x - 13107.2 = 0.
To solve this cubic equation, we can use numerical methods or a graphing calculator.
Using a graphing calculator, we find that x ≈ 18.25 inches.
The width = x ≈ 18.25 inches.
The length = x + 5 ≈ 18.25 + 5 ≈ 23.25 inches.
The height = 3x - 1 ≈ 3(18.25) - 1 ≈ 54.75 - 1 ≈ 53.75 inches.
Thus, the dimensions of the shipping box are approximately 18.25 x 23.25 x 53.75 inches.