Difference between revisions of "User:Azjps/1951 AHSME Problems/Problem 3"
(by correct, do you mean the answer or the question? The answer's right, duno about the question) |
m (1951 AHSME Problems/Problem 3 moved to User:Azjps/1951 AHSME Problems/Problem 3: well, this obviously isn't the right question ... move to userspace until we find where it does belong) |
(No difference)
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Revision as of 19:46, 10 January 2008
Problem
Points 
and 
are selected on the graph of 
so that triangle 
is equilateral. Find the length of one side of triangle (point 
is at the origin).
Solution
The parabola opens downward, and by symmetry we realize that the y-coordinates of 
are the same. Thus the segments 
will have slope 
. Without loss of generality consider the equation of 
(we let be in the third quadrant), which has equation 
. This intersects the graph of 
at 
; we drop zero so 
. The length of a side of the triangle is 
. We can now easily verify that this triangle indeed is equilateral.
See Also
| 1951 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
