Question

15 points. Given a rectangular prism with width and height = 4x and length = 10x-6. The expression for the surface area of the rectangular prism shown in the picture is 2[(4x)(4x)]+4[(10x - 6)(4x)]. Simplify this expression. a. 16x240x2 - 24x b. 32x + 160x – 96 c. 32x2 + 160x2 – 96x d. 16x + 40x – 24

Answer 1

Explanation:

Answer 2

C. 32x² + 160x² - 96x

Explanation:

Surface area of rectangular prism is given as 2(wl + hl + hw), where:

w = width = 4x

l = (10x - 6)

h = 4x

Surface area = 2[(4x)(10x - 6) + (4x)(10x - 6) + (4x)(4x)]

= 2[40x² - 24x + 40x² - 24x + 16x²]

Combine like terms

= 2[40x² + 40x² + 16x² - 24x - 24x]

= 2[96x² - 48x]

= 2(96x²) - 2(48x)

= 192x² - 96x

192x² - 96x = 32x² + 160x² - 96x

The answer is C. 32x² + 160x² - 96x