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Difference between revisions of "1986 AIME Problems/Problem 15"

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== Problem ==
 
== Problem ==
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Let triangle <math>\displaystyle ABC</math> be a right triangle in the xy-plane with a right angle at <math>\displaystyle C_{}</math>. Given that the length of the hypotenuse <math>\displaystyle AB</math> is <math>\displaystyle 60</math>, and that the medians through <math>\displaystyle A</math> and <math>\displaystyle B</math> lie along the lines <math>\displaystyle y=x+3</math> and <math>\displaystyle y=2x+4</math> respectively, find the area of triangle <math>\displaystyle ABC</math>.
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Let [[triangle]] <math>\displaystyle ABC</math> be a [[right triangle]] in the xy-plane with a right angle at <math>\displaystyle C_{}</math>. Given that the length of the [[hypotenuse]] <math>\displaystyle AB</math> is <math>\displaystyle 60</math>, and that the [[median]]s through <math>\displaystyle A</math> and <math>\displaystyle B</math> lie along the lines <math>\displaystyle y=x+3</math> and <math>\displaystyle y=2x+4</math> respectively, find the area of triangle <math>\displaystyle ABC</math>.
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== Solution ==
 
== Solution ==
 
{{solution}}
 
{{solution}}
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== See also ==
 
== See also ==
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{{AIME box|year=1986|num-b=10|after=Last Question}}
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{{AIME box|year=1986|num-b=14|after=Last Question}}
 
* [[AIME Problems and Solutions]]
 
* [[AIME Problems and Solutions]]
 
* [[American Invitational Mathematics Examination]]
 
* [[American Invitational Mathematics Examination]]
 
* [[Mathematics competition resources]]
 
* [[Mathematics competition resources]]
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 +
[[Category:Intermediate Geometry Problems]]

Revision as of 16:55, 6 May 2007

Problem

Let triangle $\displaystyle ABC$ be a right triangle in the xy-plane with a right angle at $\displaystyle C_{}$. Given that the length of the hypotenuse $\displaystyle AB$ is $\displaystyle 60$, and that the medians through $\displaystyle A$ and $\displaystyle B$ lie along the lines $\displaystyle y=x+3$ and $\displaystyle y=2x+4$ respectively, find the area of triangle $\displaystyle ABC$.

Solution

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See also

1986 AIME (Problems • Answer Key • Resources)
Preceded by
Problem 14 		Followed by
Last Question
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All AIME Problems and Solutions
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