1984 AIME Problems/Problem 3: Difference between revisions
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== Problem == | == Problem == | ||
A point <math>\displaystyle P</math> is chosen in the interior of <math>\displaystyle \triangle ABC</math> such that when | A [[point]] <math>\displaystyle P</math> is chosen in the interior of <math>\displaystyle \triangle ABC</math> such that when [[line]]s are drawn through <math>\displaystyle P</math> [[parallel]] to the sides of <math>\displaystyle \triangle ABC</math>, the resulting smaller [[triangle]]s <math>\displaystyle t_{1}</math>, <math>\displaystyle t_{2}</math>, and <math>\displaystyle t_{3}</math> in the figure, have [[area]]s <math>\displaystyle 4</math>, <math>\displaystyle 9</math>, and <math>\displaystyle 49</math>, respectively. Find the area of <math>\displaystyle \triangle ABC</math>. | ||
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== Solution == | == Solution == | ||
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* [[1984 AIME Problems/Problem 4 | Next problem]] | * [[1984 AIME Problems/Problem 4 | Next problem]] | ||
* [[1984 AIME Problems]] | * [[1984 AIME Problems]] | ||
[[Category:Intermediate Geometry Problems]] | |||
Revision as of 11:13, 24 January 2007
Problem
A point 
is chosen in the interior of 
such that when lines are drawn through parallel to the sides of , the resulting smaller triangles 
, 
, and 
in the figure, have areas 
, 
, and 
, respectively. Find the area of .
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Solution
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