Answer: 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
