The volume of a rectangular prism is 6×3 + 25×2 + 21x − 10. The length of the prism is 2x + 5. The width of the prism is 3x − 1. What is an

Question

The volume of a rectangular prism is 6×3 + 25×2 + 21x − 10. The length of the prism is 2x + 5. The width of the prism is 3x − 1. What is an expression for the height of the prism?

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Hadley 3 months 2022-02-12T01:49:32+00:00 1 Answer 0 views 0

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    2022-02-12T01:50:49+00:00

    Expression for the height of the prism is x + 2

    Solution:

    Given that,

    [tex]Volume\ of\ a\ rectangular\ prism = 6x^3+25x^2 + 21x – 10[/tex]

    [tex]Length\ of\ prism = 2x + 5[/tex]

    [tex]Width\ of\ prism = 3x-1[/tex]

    To find: height of prism

    The volume of rectangular prism is given by formula:

    [tex]Volume = length \times width \times height[/tex]

    Solving for height we get,

    [tex]height = \frac{volume}{length \times width}[/tex]

    Substituting the values we get,

    [tex]height = \frac{6x^3+25x^2+21x-10}{(2x+5)(3x-1)}[/tex]

    Factor the numerator

    [tex]height = \frac{(x+2)(3x-1)(2x+5)}{(2x+5)(3x-1)}[/tex]

    Cancel the common factors,

    [tex]height = x + 2[/tex]

    Thus expression for the height of the prism is x + 2

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