Difference between revisions of "2015 AMC 10B Problems/Problem 13"
(Created page with "We find the x-intercepts and the y-intercepts to find the intersections of the axes and the line. If <math>x=0</math>, then <math>y=12</math>. If <math>y</math> is <math>0</ma...") |
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− | We find the x-intercepts and the y-intercepts to find the intersections of the axes and the line. If <math>x=0</math>, then <math>y=12</math>. If <math>y</math> is <math>0</math>, then <math>x=5</math>. Our three vertices are <math>(0,0)</math>, <math>(5,0)</math>, and <math>(0,12)</math>. | + | We find the x-intercepts and the y-intercepts to find the intersections of the axes and the line. If <math>x=0</math>, then <math>y=12</math>. If <math>y</math> is <math>0</math>, then <math>x=5</math>. Our three vertices are <math>(0,0)</math>, <math>(5,0)</math>, and <math>(0,12)</math>. Two of our altitudes are <math>5</math> and <math>12</math>. Since the area of the triangle is <math>30</math>, our final altitude has to be <math>30</math> divided by the hypotenuse. By the Pythagorean Theorem, our hypotenuse is <math>13</math>, so the sum of our altitudes is <math>\boxed{281/13}</math>. |
Revision as of 23:37, 3 March 2015
We find the x-intercepts and the y-intercepts to find the intersections of the axes and the line. If , then . If is , then . Our three vertices are , , and . Two of our altitudes are and . Since the area of the triangle is , our final altitude has to be divided by the hypotenuse. By the Pythagorean Theorem, our hypotenuse is , so the sum of our altitudes is .