Answer: the height = 14 inches
Width = 13 inches
Explanation:
Let h represent the height of the storage box.
The height of the box will be 1 in. more than its width. This means that the width of the box would be (h - 1) inch.
The formula for determining the volume of a rectangular box is expressed as
Volume = length × width × height
From the information given,
Volume = 4368 in³
Length = 24 in
Therefore,
4368 = 24 × h × (h - 1)
4368 = 24h(h - 1)
Dividing both sides by 24, it becomes
182 = h² - h
h² - h - 182 = 0
h² + 13h - 14h - 182 = 0
h(h + 13) - 14(h + 13) = 0
h - 14 = 0 or h + 13 = 0
h = 14 or h = - 13
Since the height cannot be negative, then h = 14 inches
Width = h - 1 = 14 - 1
Width = 13 inches