Difference between revisions of "2002 AMC 12P Problems/Problem 9"
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| + | {{duplicate|[[2002 AMC 12P Problems|2002 AMC 12P #9]] and [[2002 AMC 10P Problems|2002 AMC 10P #16]]}} | ||
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== Problem == | == Problem == | ||
Two walls and the ceiling of a room meet at right angles at point <math>P.</math> A fly is in the air one meter from one wall, eight meters from the other wall, and nine meters from point <math>P</math>. How many meters is the fly from the ceiling? | Two walls and the ceiling of a room meet at right angles at point <math>P.</math> A fly is in the air one meter from one wall, eight meters from the other wall, and nine meters from point <math>P</math>. How many meters is the fly from the ceiling? | ||
Revision as of 16:29, 14 July 2024
- The following problem is from both the 2002 AMC 12P #9 and 2002 AMC 10P #16, so both problems redirect to this page.
Problem
Two walls and the ceiling of a room meet at right angles at point 
A fly is in the air one meter from one wall, eight meters from the other wall, and nine meters from point 
. How many meters is the fly from the ceiling?
Solution
We can use the formula for the diagonal of a rectangular prism, or 
The problem gives us 
and 
Solving gives us 
See also
| 2002 AMC 12P (Problems • Answer Key • Resources) | |
| Preceded by Problem 8 |
Followed by Problem 10 |
| 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 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
