Question

a rectangular prism has dimensions x units, 2x units, and x + 8 units. which expression represents the surface area of the prism? 8x + 16 square units 16x + 32 square units 10x² + 48x square units 2x³ + 16x² square units

Explanation:

Step1: Recall surface area formula

The surface area $S$ of a rectangular prism with length $l$, width $w$, height $h$ is $S=2(lw+lh+wh)$.

Step2: Assign given dimensions

Let $l=x$, $w=2x$, $h=x+8$.

Step3: Calculate each pair product

• $lw = x \times 2x = 2x^2$
• $lh = x \times (x+8) = x^2+8x$
• $wh = 2x \times (x+8) = 2x^2+16x$

Step4: Sum the products

$lw+lh+wh = 2x^2 + (x^2+8x) + (2x^2+16x) = 5x^2+24x$

Step5: Multiply by 2

$S = 2(5x^2+24x) = 10x^2+48x$

Answer:

10$x^2$ + 48$x$ square units