Question

The volume of a rectangular prism is given by the expression10x3 + 46x2 – 21x – 27. The area of the base of the prism is given by the expression 2x2 + 8x – 9. Which of the following expressions represents the height of the prism? (V = Bh)
a) 8x - 3
b) 3x - 5
c) 5x + 3
d) 42x + 3

Answer 1

Answer:

The correct option is c.

Step-by-step explanation:

The volume of a rectangular prism is given by the expression

$V=10x^3+46x^2-21x-27$

The area of the base of the prism is given by the expression

$B=2x^2+8x-9$

The volume of a rectangular prism is

$V=Bh$

Where, B is base area and h is height of the prism. Divide both the sides by B.

$\frac{V}{B}=h$

So, the height of the prism is

$h=\frac{V}{B}=\frac{10x^3+46x^2-21x-27}{2x^2+8x-9}$

Factories the numerator.

$h=\frac{ (5 x + 3)(2 x^2 + 8 x - 9) }{2x^2+8x-9}$

Cancel out the common factors.

$h=5 x + 3$

The height of the prism is 5x+3. Therefore the correct option is c.

Answer 2

Height  = volume / area of the base
            = 10x^3 + 46x^2 - 21x - 27 /  2x^2 + 8x - 9

   10x^3 / 2x^2  = 5x  so the first term  in the answer will be 5x

Answer is   (c).