2002 AMC 12P Problems/Problem 9

Revision as of 01:04, 31 December 2023 by Wes (talk | contribs) (Solution)

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 the rectangle, or $\sqrt{a^2+b^2+c^2}=d$ The problem gives us $a=1, b=8,$ and $c=9.$ Solving gives us $\sqrt{1^2 + 8^2 + c^2}=9 \implies c^2=9^2-8^2-1^2 \implies c^2=16 \implies c=\boxed{\textbf{(D) } 4.$ (Error compiling LaTeX. Unknown error_msg) 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?

See also

2002 AMC 12P (ProblemsAnswer KeyResources)
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

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