Question

The areas of three different faces of a rectangular prism are 18 cm^2 , 48 cm^2, and 96 cm^2. what is the volume of the prism?

Answer 1

Suppose the x, y, and z represent the three dimensions of the rectangular prism, then xy=18, xz = 48, and yz = 96.

Answer 2

We have three equations and three unknowns, so we can solve for x, y, and z.

Answer 3

Since xz = 48, z = 48/x
Substitute that into yz = 96 to get y*48/x = 96.
Divide both sides by 48 and y/x = 2, or y = 2x.

Answer 4

Substitute y = 2x into xy = 18 to get 2x^2 = 18.
Divide by 2 and x^2 = 9.
x = -3 or 3.

Answer 5

what's the next step? Please solve it