Here, we are required to determine the width of the delivery box given the dimensions as in the question.
The <em>correct</em> answer is choice A.
The width of the delivery box is ; w = 7.
A <em>rectangular box</em> had the shape of a cuboid.
Volume of a <em>cuboid</em> = <em>Length</em> × <em>width</em> × <em>height</em>
<em>width</em> = w
<em>Length</em> = 2w - 6
<em>height</em> = w - 2
280 = (w) × (2w - 6) × (w - 2)
280 = (2w² - 6w) × (w - 2)
280 = 2w³ - 4w² - 6w² + 12w
280 = 2w³ - 10w² + 12w
2w³ - 10w² + 12w - 280 = 0
Therefore, w³ - 5w² + 6w - 140 = 0
By testing hypothesis at w = 7, i.e (w - 7) is a factor.
The expression cam be factorized as;
(w - 7)(w² +2w + 20) = 0.
Therefore, the only real solution of w is , w = 7.
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