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