2016 AMC 10B Problems/Problem 9
Contents
[hide]Problem
All three vertices of lie on the parabola defined by , with at the origin and parallel to the -axis. The area of the triangle is . What is the length of ?
Solution
The area of the triangle is , so , giving a total distance across the top of , which is answer .
Solution 2 (Guess and Check)
Let the point where the height of the triangle intersects with the base be . Now we can guess what is and find . If is , then is . The cords of and would be and , respectively. The distance between and is , meaning the area would be , not . Now we let . would be . The cords of and would be and , respectively. would be , and the height would be . The area would then be which is , so is .
Video Solution (CREATIVE THINKING)
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Video Solution
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See Also
2016 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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