The length of the rectangular prism obtained by finding the quotient of the volume divided by the product of height and width. Hence, the length of the box is x + 4
The volume of a rectangular prism is given calculated using the formula :
Volume = Length × width × height
- Width = x - 1
- Height = x + 8
- Volume = x³ + 11x² + 20x – 32.
From the formula :
Length = \(\frac{volume} {width \times height}\)
Width × height = (x - 1)(x + 8)
(x - 1)(x + 8) = x² + 8x - x - 8
= x² + 7x - 8
- Divisor = x² + 7x - 8
- Dividend = x³ + 11x² + 20x – 32
Using long divison :
______ | x + 4
______ | _______________
x²+7x-8 | x³ + 11x² + 20x – 32
______ | x³ + 7x² - 8x
-______| ___ 4x²+28x
___________4x²+28x - 32
-___________0__0 ___0
Therefore, the quotient, which is the value of the length of the rectangular prism ls x + 4
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