26 August, 02:37

# 5. 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 f3. Find the dimensions of the box in inches. Round to the nearest inch. (Hint: 1 f 1,728 in. 3)

+1
1. 26 August, 06:23
0
The volume of a cuboid is given by length * width * height

We have:

Volume = 7.6 ft³

Height = 3x - 1

Length = x + 5

Width = x

Substituting these into the formula, we have:

7.6 = (3x - 1) (x + 5) (x)

7.6 = [3x² + 15x - x - 5] (x)

7.6 = [3x² + 14x - 5] (x)

7.6 = 3x³ + 14x² - 5x

0 = 3x³ + 14x² - 5x - 7.6

Drawing the graph is one way of finding the solution (refer to the graph below):

We have three solutions (where the curve crosses the x-axis):

x = - 4.9

x = - 0.6

x = 0.8

Putting these solutions back into the context, since we are looking for the value of x which is part of measurement of length, we cannot have negative value, so we will take the value of x = 0.8 ft

Converting 0.8 ft into inches = 0.8 * 12 inches = 9.6 inches

Answer: x = 9.6 inches