Difference between revisions of "1995 AIME Problems/Problem 11"
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== Problem == | == Problem == | ||
| + | A right rectangular prism <math>\displaystyle P_{}</math> (i.e., a rectangular parallelpiped) has sides of integral length <math>\displaystyle a, b, c,</math> with <math>\displaystyle a\le b\le c.</math> A plane parallel to one of the faces of <math>\displaystyle P_{}</math> cuts <math>\displaystyle P_{}</math> into two prisms, one of which is similar to <math>\displaystyle P_{},</math> and both of which have nonzero volume. Given that <math>\displaystyle b=1995,</math> for how many ordered triples <math>\displaystyle (a, b, c)</math> does such a plane exist? | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1995_AIME_Problems/Problem_10|Previous Problem]] | ||
| + | * [[1995_AIME_Problems/Problem_12|Next Problem]] | ||
* [[1995 AIME Problems]] | * [[1995 AIME Problems]] | ||
Revision as of 00:25, 22 January 2007
Problem
A right rectangular prism 
(i.e., a rectangular parallelpiped) has sides of integral length 
with 
A plane parallel to one of the faces of cuts into two prisms, one of which is similar to 
and both of which have nonzero volume. Given that 
for how many ordered triples 
does such a plane exist?
