The length of a base of a rectangular prism is twice the width of the base. the height of the prism is 3 times the width of a base. the surface area is 792 square centimeters. what are the dimensions of the prism?

The dimensions of the rectangular prism is

6cm by 12cm by 18cm [width, length and height] respectively

Step-by-step explanation:

In this question, we are asked to calculate the dimensions of a right prism given the information in the question.

Mathematically, for a right prism, the surface area is as follows;

A = 2 (wl + lh + hw)

Where l, h and w represent the length, height and width respectively.

Now let's pull the information from the question to get the dimensions.

Length is twice the width, that means l = 2w

Height is 3 times the width, that means h = 3w

Now let's plug these two into the surface area equation, it becomes;

A = 2 (2w (w) + 2w (3w) + w (3w))

A = 2 (2w^2 + 6w^2 + 3w^2)

A = 2 (11w^2)

A = 22w^2

Let's insert what the value of the area is

792 = 22w^2

w^2 = 792/22

w^2 = 36

w = sqr. root 36

w = 6cm

We ignore the - 6 square root answer as length cannot be negative

l = 2w = 2 (6) = 12cm

w = 3w = 3 (6) = 18cm