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? | |
− | <math> \ | + | <math>\text{(A) }\sqrt{13} \qquad \text{(B) }\sqrt{14} \qquad \text{(C) }\sqrt{15} \qquad \text{(D) }4 \qquad \text{(E) }\sqrt{17}</math> |
== Solution == | == Solution == | ||
− | + | We can use the formula for the diagonal of a rectangular prism, or <math>d=\sqrt{a^2+b^2+c^2}</math> The problem gives us <math>a=1, b=8,</math> and <math>d=9.</math> Solving gives us <math>9=\sqrt{1^2 + 8^2 + c^2} \implies c^2=9^2-8^2-1^2 \implies c^2=16 \implies c=\boxed{\textbf{(D) } 4}.</math> | |
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+ | ~Minor edits by Astro2010~ | ||
== See also == | == See also == | ||
+ | {{AMC10 box|year=2002|ab=P|num-b=15|num-a=17}} | ||
{{AMC12 box|year=2002|ab=P|num-b=8|num-a=10}} | {{AMC12 box|year=2002|ab=P|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 13:46, 9 August 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
~Minor edits by Astro2010~
See also
2002 AMC 10P (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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 10 Problems and Solutions |
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.