Difference between revisions of "2002 AIME II Problems/Problem 2"

Revision as of 19:43, 3 November 2007

Three vertices of a cube are $P=(7,12,10)$ , $Q=(8,8,1)$ , and $R=(11,3,9)$ . What is the surface area of the cube?

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 == Problem ==
-The diagram shows twenty congruent circles arranged in three rows and enclosed in a rectangle.  The circles are tangent to one another and to the sides of the rectangle as shown in the diagram.  The ratio of the longer dimension of the rectangle to the shorter dimension can be written as <math>\frac{1}{2}\left(\sqrt{p}-q\right),</math> where <math>p</math> and <math>q</math> are positive integers.  Find <math>p+q.</math>
+Three vertices of a cube are <math>P=(7,12,10)</math>, <math>Q=(8,8,1)</math>, and <math>R=(11,3,9)</math>. What is the surface area of the cube?
-{{image}} (the image needed is image 6601 in the Album.)
 == Solution ==
 {{solution}}