Question

The volume of a square prism is 144x^3 +216x^2 +81x

What is an expression that could describe the perimeter of one of the prism's square faces? Please state the steps in word form. Will give 25 points

Answer 1

Equation for the perimeter of prism's square face: 16x + 12

Explanation:

Volume of Square prism = Length * Width * Height

= 144 x^3 + 216 x^2 +81 x

taking 9x common = 9x( 16 x^2 + 24 x + 9)

= 9x ( (4x)^2 + 2(4x)(3) + (3)^2 )

= 9x ( 4x+3)^2

so the length is 9x, width is 4x+3 and height is 4x+3

Now, Perimeter of prism's square face = 2* Width + 2 * Height

= 2* (4x+3) + 2* (4x+3)

= 8x +6 + 8x + 6

= 16x +12