The volume of a 15-oz cereal box is 180.4 in.3. The length of the box is 3.2 in. less than the height, and its width is 2.3 in. Find the height and length of the box to the nearest tenth.

length = 4.2 inches

Height = 7.4 inches

Step-by-step explanation:

Let H represent the height of the cereal box

The formula for determining the volume of a rectangular box is expressed as

Volume = LWH

From the information given,

Volume of the box = 180.4 inches³

The length of the box is 3.2 in. less than the height. It means that

L = H - 3.2

Width, W = 2.3 inches

Therefore,

180.4 = (H - 3.2) × h × 2.3

H(H - 3.2) = 180.4/2.3

H(H - 3.2) = 78.4

H² - 3.2H - 78.4 = 0

We would apply general formula for solving quadratic equations which is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 1

b = - 3.2

c = - 78.4

Therefore,

H = [- - 3.2 ± √(- 3.2² - 4 × 1 × - 78.4)]/2 × 1

H = [3.2 ± √(10.24 - - 313.6)]/2

H = [3.2 ± √323.84]/2

H = (- 3.2 + 18)/2 or x = (- 3.2 - 18)/2

H = 14.8/2 or H = - 21.2/2

H = 7.4 or H = - 10.6

Since the height cannot be negative, then H = 7.4 inches

Length = 7.4 - 3.2 = 4.2 inches