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

Revision as of 07:48, 17 April 2008

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?

$PQ=\sqrt{(8-7)^2+(8-12)^2+(1-10)^2}=\sqrt{98}$

$PR=\sqrt{(11-7)^2+(3-12)^2+(9-10)^2}=\sqrt{98}$

$QR=\sqrt{(11-8)^2+(3-8)^2+(9-1)^2}=\sqrt{98}$

So, PQR is an equilateral triangle. Let the side of the cube is $a$ . $a\sqrt{2}=\sqrt{98}$

So, $a=7$ , and hence the surface area= $6a^2=294$ .

@@ Line 14: / Line 14: @@
 So, <math>a=7</math>, and hence the surface area=<math>6a^2=294</math>.
 == See also ==
-* [[2002 AIME II Problems/Problem 1 | Previous problem]]
+{{AIME box|year=2002|n=II|num-b=1|num-a=3}}
-* [[2002 AIME II Problems/Problem 3 | Next problem]]
 * [[2002 AIME II Problems]]

2002 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All AIME Problems and Solutions