Difference between revisions of "2002 AMC 12P Problems/Problem 9"
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== Solution == | == Solution == | ||
We can use the formula for the diagonal of the rectangle, or <math>\sqrt{a^2+b^2+c^2}=d</math> The problem gives us <math>a=1, b=8,</math> and <math>c=9.</math> Solving gives us <math>\sqrt{1^2 + 8^2 + c^2}=9 \implies c^2=9^2-8^2-1^2 \implies c^2=16 \implies c=\boxed{\textbf{(D) } 4}.</math> | We can use the formula for the diagonal of the rectangle, or <math>\sqrt{a^2+b^2+c^2}=d</math> The problem gives us <math>a=1, b=8,</math> and <math>c=9.</math> Solving gives us <math>\sqrt{1^2 + 8^2 + c^2}=9 \implies c^2=9^2-8^2-1^2 \implies c^2=16 \implies c=\boxed{\textbf{(D) } 4}.</math> | ||
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== See also == | == See also == | ||
{{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}} | ||
Revision as of 01:05, 31 December 2023
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 the rectangle, 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. 
