[Solved!]Given volume and SA, find lengths.
Given volume and surface area of a rectangular solid, and sides are in GP.?
The volume of a certain recangular solid is 64 and its total surface area is 384. Its three dimensions are in geometric progression. What is the sum of the lengths of all the edges of this solid.
I myself don't really understand what the last sentence means, but I believe its something like finding the perimeter, but of a 3D object. Anyway, since the sides are in a GP, I know that the sides are x, xr, and xr². Using the volume formula, you can simplify to get
I'm having trouble with the surface area part, as when I substitute this x value into the forumla
( ), I get a quadratic which has two different values for r, but I am pretty sure there is only supposed to be one value for r, otherwise there would be MANY solutions to this question. Thanks in advance for any help.