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