Based on the calculations, the width and height of this rectangular prism are 7 inches and 10 inches respectively.
Mathematically, the volume of a rectangular prism can be calculated by using this formula:
V = L × W × H
Where:
Given the following data:
Length = 4 in.
Width = (n + 2) in.
Height = (n + 5) in.
Substituting the given parameters into the formula, we have;
280 = 4 × (n + 2) × (n + 5)
280 = 4 × (n² + 7n + 10)
60 = n² + 7n + 10
n² + 7n - 60 = 0
(n - 5)(n + 12) = 0
Therefore, n = 5 or -12.
For the width, we have:
Width = n + 2
Width = 5 + 2
Width = 7 in.
For the height, we have:
Height = n + 5
Height = 5 + 5
Height = 10 in.
Read more on rectangular prism here: brainly.com/question/3867601
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Complete Question:
A box shaped like a rectangular prism has a volume of 280 in³. Its dimensions are 4 in. by (n + 2) in. by (n + 5) in. Find n.
