Difference between revisions of "1984 AIME Problems/Problem 3"
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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>. |
− | + | {{image}} | |
== Solution == | == Solution == | ||
{{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]] | ||
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+ | [[Category:Intermediate Geometry Problems]] |
Revision as of 12:13, 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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