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Answer :
Final answer:
The width of the prism is (6-2) = 4 inches and the height is (6+3) = 9 inches.
Explanation:
To find the width and height of the prism, we need to solve for x in the equation: (Length) * (Width) * (Height) = Volume. Given that the length is 5 inches, the width is (x-2) inches, and the height is (x+3) inches, we can substitute these values into the equation and solve for x:
(5) * (x-2) * (x+3) = 120
Expanding this equation gives: 5x2 + 5x - 30 = 120
Simplifying further, we have: 5x2 + 5x - 150 = 0
Factoring this equation gives: (x-6)(5x+25) = 0
Setting each factor equal to zero gives: x-6 = 0 or 5x+25 = 0
Solving these equations gives: x = 6 or x = -5
Since the width and height cannot be negative, the only valid solution is x = 6.
Therefore, the width of the prism is (6-2) = 4 inches and the height is (6+3) = 9 inches.
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