Difference between revisions of "2019 Mock AMC 10B Problems/Problem 5"
Awesome 360 (talk | contribs) (Created page with "The intersection of the medians in a triangle is the centroid, which splits each median into a 2:1 ratio. Also, in an equilateral triangle, each median divides the opposite le...") |
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| − | The intersection of the medians in a triangle is the centroid, which splits each median into a 2:1 ratio. Also, in an equilateral triangle, each median divides the opposite leg into 2 equal parts, so we can find the length of each median by the Pythagorean theorem - We have a right triangle with legs 1 and 1/2, so the length of the other leg (the median) is | + | The intersection of the medians in a triangle is the centroid, which splits each median into a 2:1 ratio. Also, in an equilateral triangle, each median divides the opposite leg into 2 equal parts, so we can find the length of each median by the Pythagorean theorem - We have a right triangle with legs 1 and 1/2, so the length of the other leg (the median) is (sqrt3)/2. |
| − | Let 2x be the length of PA/PB/PC, and x= the length of the other part of the median. Solving for x, we have x= sqrt3/6, and 2x= sqrt3/3. 3(sqrt3)/3= sqrt3. The answer is (D). | + | Let 2x be the length of PA/PB/PC, and x= the length of the other part of the median. Solving for x, we have x= (sqrt3)/6, and 2x= (sqrt3)/3. 3(sqrt3)/3= sqrt3. The answer is (D). |
~Awesome_360 | ~Awesome_360 | ||
Latest revision as of 21:43, 9 April 2021
The intersection of the medians in a triangle is the centroid, which splits each median into a 2:1 ratio. Also, in an equilateral triangle, each median divides the opposite leg into 2 equal parts, so we can find the length of each median by the Pythagorean theorem - We have a right triangle with legs 1 and 1/2, so the length of the other leg (the median) is (sqrt3)/2.
Let 2x be the length of PA/PB/PC, and x= the length of the other part of the median. Solving for x, we have x= (sqrt3)/6, and 2x= (sqrt3)/3. 3(sqrt3)/3= sqrt3. The answer is (D).
~Awesome_360
