Difference between revisions of "1950 AHSME Problems/Problem 21"
m |
(→See Also) |
||
| Line 21: | Line 21: | ||
==See Also== | ==See Also== | ||
| − | {{AHSME box|year=1950|num-b=20|num-a=22}} | + | {{AHSME 50p box|year=1950|num-b=20|num-a=22}} |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 08:33, 29 April 2012
Problem
The volume of a rectangular solid each of whose side, front, and bottom faces are 
, 
, and 
respectively is:
Solution
If the sidelengths of the cubes are expressed as 
and 
then we can write three equations:
![\[ab=12, bc=8, ac=6.\]](http://latex.artofproblemsolving.com/4/2/3/423226df7be3000ec5f1ded053b7c2595014f3bf.png)
The volume is 
Notice symmetry in the equations. We can find 
my multiplying all the equations and taking the positive square root.
See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
