Question

the net of a rectangular prism is shown below. the surface area of each face is labeled. which values represent the dimensions, in feet, of the rectangular prism? (note: diagram is not to scale) answer 4,8,10 8,20,40 2,4,10 4,8,16

Explanation:

Step1: Recall area - formula for rectangle

The area of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Let the dimensions of the rectangular - prism be $a$, $b$, and $c$. The faces of the rectangular prism have areas $ab$, $ac$, and $bc$.

Step2: Check the product of values in each option

• Option A: If the dimensions are $4$, $8$, and $10$. Then $4\times8 = 32

eq8$, $4\times10 = 40$, $8\times10 = 80
eq20$.

• Option B: If the dimensions are $8$, $20$, and $40$. Then $8\times20 = 160

eq8$, $8\times40 = 320
eq20$, $20\times40 = 800
eq40$.

• Option C: If the dimensions are $2$, $4$, and $10$. Then $2\times4 = 8$, $2\times10 = 20$, $4\times10 = 40$.
• Option D: If the dimensions are $4$, $8$, and $16$. Then $4\times8 = 32

eq8$, $4\times16 = 64
eq20$, $8\times16 = 128
eq40$.

Answer:

$2,4,10$