Question

if the volume of a right rectangular prism is 1.5 inches ^3 and its length and width have a product of 1.5in squared, what is the height of the prism?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's say the length of the prism is L inches, the width is W inches, and the height is H inches.

We are given that the volume of the prism is 1.5 in^3, so we have:

V = LWH = 1.5

We are also given that the product of the length and width is 1.5 in^2, so we have:

LW = 1.5

We can solve the second equation for one of the variables, substitute it into the volume equation, and solve for the height:

LW = 1.5
L = 1.5/W

Substitute L = 1.5/W into the volume equation:

V = LWH = 1.5
1.5/W * W * H = 1.5
1.5H = 1.5
H = 1.5 / 1.5
H = 1

Therefore, the height of the prism is 1 inch.