Difference between revisions of "1985 AHSME Problems/Problem 25"
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Revision as of 12:01, 5 July 2013
Problem
The volume of a certain rectangular solid is 
, its total surface area is 
, and its three dimensions are in geometric progression. The sums of the lengths in cm of all the edges of this solid is
Solution
Let the side lengths be 
. Thus, the volume is 
, so 
and the side lengths can be written as 
.
The surface area is 
Both values of 
give the same side length, the only difference is that one makes them count up and one makes them count down. We pick 
. (The solution proceeds the same had we picked 
). Thus, the side lengths are
We have the sum of the distinct side lengths is 
, and since each side length repeats 
times, the total sum is 
.
See Also
| 1985 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Problem 26 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
