A storage box of volume 4368 in. The length of the box will be 24 in. The height of the box will be 1 in. More than its width. Find the height and width of the box

Answer: the height = 14 inches

Width = 13 inches

Step-by-step 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