Respuesta :
Answer:
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
