SOLUTION: The ratio of the dimensions of a rectangular solid is 5:4:3, and the ratio of this solid's volume to its surface area is 2:1. What is the length of the solid's shortest side?

Question 283621: The ratio of the dimensions of a rectangular solid is 5:4:3, and the ratio of this solid's volume to its surface area is 2:1. What is the length of the solid's shortest side?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
The sides of of rectangular solid are (LWH) in proportion 5:4:3
We don't know which sides are which.
volume =L*H*W
There are six surface areas. Two of each
LW+LW+HW+HW+LH+LH
2LW+2HW+2LH
5x=L
4x=W
3x=H
A=2*(LW+HW+LH)
V =LWH
V/A=2/1
5x=L,4x=W,3x=H, (L*W*H)/(2*(L*W+H*W+L*H))=2/1
H = 47/5, L = 47/3, W = 188/15, x = 47/15
H=9.4, L=15.6667, W=12.5333, x=3.13333
188/15 or 9.4 is the shortest side
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