Answered

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)

A8x - 3

B3x - 5

C5x + 3

D42x + 3

Verified Answer :

Answer

option (c) is correct .

To proof

Reason

Formula

Volume of the rectangular prism = Base × Height

The expression is in the Question be

10x ³ + 46 x² - 21x -27

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

2x² + 8x - 9 .

Put in the formula

10x ³ + 46 x² - 21x -27  = 2x² + 8x - 9  × Height

The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .

put in the formula

(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height

Cancelled 2x² + 8x - 9 on both side.

(5x+3)unit = Height

Hence proved

Answer:

The expression for the height of the prism will be \(5x+3\) .

Step-by-step explanation:

Given information

The expression for the volume of the prism

\(V =10x^3+46x^2-21x-27\)

The expression for the Area of the base of the prism

\(A=2x^2+8x-9\)

As given

Volume = base * height

Height = volume / base

\(H= \frac{(10x^3+46x^2-21x-27)}{2x^2-8x-9}\)

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

on solving above equation

\(H= 5x+3\)

Hence the expression for the height of the prism will be 5x+3 .

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