Difference between revisions of "2019 AIME II Problems/Problem 7"
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==Problem== | ==Problem== | ||
| + | Triangle <math>ABC</math> has side lengths <math>AB=120,BC=220</math>, and <math>AC=180</math>. Lines <math>\ell_A,\ell_B</math>, and <math>\ell_C</math> are drawn parallel to <math>\overline{BC},\overline{AC}</math>, and <math>\overline{AB}</math>, respectively, such that the intersections of <math>\ell_A,\ell_B</math>, and <math>\ell_C</math> with the interior of <math>\triangle ABC</math> are segments of lengths <math>55,45</math>, and <math>15</math>, respectively. Find the perimeter of the triangle whose sides lie on lines <math>\ell_A,\ell_B</math>, and <math>\ell_C</math>. | ||
==Solution== | ==Solution== | ||
Revision as of 18:24, 22 March 2019
Problem
Triangle 
has side lengths 
, and 
. Lines 
, and 
are drawn parallel to 
, and 
, respectively, such that the intersections of , and with the interior of 
are segments of lengths 
, and 
, respectively. Find the perimeter of the triangle whose sides lie on lines , and .
Solution
See Also
| 2019 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
