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.
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.