OG 122
What is the volume of a certain rectangular solid?
(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.
Okay, so if we look at statement one, we know that there can be a number of combinations for dimensions that fit the criteria such as 3 x 5 and 3 x 8 or 1 x 15 and 1 x 24. Also, we do not necessarily know if the two opposite sides (top and bottom of the rectangle if you will) has which surface area depending on how it is positioned.
So this part makes sense, but now if you go to statement 2, each of two opposite faces has area of 40. Doesn't a rectangle only have two identical opposite sides and four similar identical sides? If we take both statements together, it seems like there are three sides (area of 40, 24 and 15).
Someone please let me know where my logic fails here.
What is the volume of a certain rectangular solid?
(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.
Okay, so if we look at statement one, we know that there can be a number of combinations for dimensions that fit the criteria such as 3 x 5 and 3 x 8 or 1 x 15 and 1 x 24. Also, we do not necessarily know if the two opposite sides (top and bottom of the rectangle if you will) has which surface area depending on how it is positioned.
So this part makes sense, but now if you go to statement 2, each of two opposite faces has area of 40. Doesn't a rectangle only have two identical opposite sides and four similar identical sides? If we take both statements together, it seems like there are three sides (area of 40, 24 and 15).
Someone please let me know where my logic fails here.
