Answer: 7
Step-by-step explanation:
Length : 6 - x2
Height : x - 2
Width : x = 7
Formula for a rectangle : H x L x W
280 = (7)2 - 6 x (7) - 2 x 7
280 = 14 - 6 x 5 x 7
280 = 8 x 5 x 7
the width of the delivery box is 7 inches
The volume of the solid box is given as:
Volume = length × width × height
Let x represent the width of the box.
The length of the delivery box is 6 inches less than twice the width, hence:
Length = 2x - 6
The height is 2 inches less than the width, hence:
Height = x - 2
Therefore:
volume = length × width × breadth
280 = (2x - 6)(x - 2)(x)
280 = (2x - 6)(x² - 2x)
2x³ - 4x² - 6x² + 12x = 280
2x³ - 10x² + 12x - 280 = 0
Therefore x = 7
Hence the width of the delivery box is 7 inches.
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