Difference between revisions of "1984 AIME Problems"
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== Problem 3 == | == Problem 3 == | ||
+ | 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>. | ||
[[1984 AIME Problems/Problem 3|Solution]] | [[1984 AIME Problems/Problem 3|Solution]] |
Revision as of 22:38, 20 January 2007
Contents
[hide]Problem 1
Find the value of if , , is an arithmetic progression with common difference 1, and .
Problem 2
The integer is the smallest positive multiple of such that every digit of is either or . Compute .
Problem 3
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 .