Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2002 AMC 12P Problems/Problem 9"
m (→‎Solution)
 
(2 intermediate revisions by 2 users not shown)
Line 7: Line 7:
  
 
== 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>c=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>
+
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>
 +
 
 +
 
 +
~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 12:46, 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 $P.$ A fly is in the air one meter from one wall, eight meters from the other wall, and nine meters from point $P$. How many meters is the fly from the ceiling?

$\text{(A) }\sqrt{13} \qquad \text{(B) }\sqrt{14} \qquad \text{(C) }\sqrt{15} \qquad \text{(D) }4 \qquad \text{(E) }\sqrt{17}$

Solution

We can use the formula for the diagonal of a rectangular prism, or $d=\sqrt{a^2+b^2+c^2}$ The problem gives us $a=1, b=8,$ and $d=9.$ Solving gives us $9=\sqrt{1^2 + 8^2 + c^2} \implies c^2=9^2-8^2-1^2 \implies c^2=16 \implies c=\boxed{\textbf{(D) } 4}.$


~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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_12P_Problems/Problem_9&oldid=224812"