Difference between revisions of "1984 AIME Problems/Problem 3"
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== Problem == | == Problem == | ||
| − | A point <math>P</math> is chosen in the interior of <math>\triangle ABC</math> such that when lines are drawn through <math>P</math> parallel to the sides of <math>\triangle ABC</math>, the resulting smaller triangles <math>t_{1}</math>, <math>t_{2}</math>, and <math>t_{3}</math> in the figure, have areas <math>4</math>, <math>9</math>, and <math>49</math>, respectively. Find the area of <math>\triangle ABC</math>. | + | A point <math>\displaystyle P</math> is chosen in the interior of <math>\displaystyle \triangle ABC</math> such that when lines are drawn through <math>\displaystyle P</math> parallel to the sides of <math>\displaystyle \triangle ABC</math>, the resulting smaller triangles <math>\displaystyle t_{1}</math>, <math>\displaystyle t_{2}</math>, and <math>\displaystyle t_{3}</math> in the figure, have areas <math>\displaystyle 4</math>, <math>\displaystyle 9</math>, and <math>\displaystyle 49</math>, respectively. Find the area of <math>\displaystyle \triangle ABC</math>. |
== Solution == | == Solution == | ||
Revision as of 00:23, 21 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 .
Solution
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