Final Answer:
The box dimensions are: height = 6 ft, length = 15 ft, and width = 2 ft.
Step-by-step explanation:
Let h be the height of the box. Then, the length is l = h + 9 and the width is w = h - 4. The volume of the box is given by:
l * w * h = 180
(h + 9) * (h - 4) * h = 180
Expanding the brackets and simplifying:
h^3 + 5h^2 - 132h + 720 = 0
Factoring the equation:
(h - 6)(h^2 + 11h - 120) = 0
Solving for h:
h = 6 (since h cannot be negative)
Therefore:
l = h + 9 = 15 ft
w = h - 4 = 2 ft
So, the box dimensions are 6 ft high, 15 ft long, and 2 ft wide.
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Complete Question
A large plywood box has a volume of 180 ft ( square). Its length is 9 ft greater than its height, and its width is 4 ft less than its height. What are the dimensions of the box?
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