## 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

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## Answers ( )

Expression for the height of the prism is x + 2Solution: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