Question

The dimensions in inches of a shipping box at You Bring It, We Ship It 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. Round to the nearest inch.

Answer 1

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