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

1. Expression for the height of the prism is x + 2

Solution:

Given that,

$$Volume\ of\ a\ rectangular\ prism = 6x^3+25x^2 + 21x – 10$$

$$Length\ of\ prism = 2x + 5$$

$$Width\ of\ prism = 3x-1$$

To find: height of prism

The volume of rectangular prism is given by formula:

$$Volume = length \times width \times height$$

Solving for height we get,

$$height = \frac{volume}{length \times width}$$

Substituting the values we get,

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

Factor the numerator

$$height = \frac{(x+2)(3x-1)(2x+5)}{(2x+5)(3x-1)}$$

Cancel the common factors,

$$height = x + 2$$

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