Difference between revisions of "2016 AMC 10B Problems/Problem 9"
Mathking999 (talk | contribs) (→Solution) |
|||
Line 17: | Line 17: | ||
label("$r$",(0,17)--(4,17),N); | label("$r$",(0,17)--(4,17),N); | ||
</asy> | </asy> | ||
− | The area of the triangle is <math>r^3</math>, so <math>r^3=64\implies r=4</math>, giving a total distance across the top of <math>8</math>, which is answer <math>\textbf{(C)}</math>. | + | The area of the triangle is <math>\frac{(2r)(r^2)}{2} = r^3</math>, so <math>r^3=64\implies r=4</math>, giving a total distance across the top of <math>8</math>, which is answer <math>\textbf{(C)}</math>. |
==Video Solution== | ==Video Solution== |
Revision as of 09:23, 5 September 2021
Contents
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 .
Video Solution
~savannahsolver
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.