Difference between revisions of "1950 AHSME Problems/Problem 9"
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Revision as of 13:27, 17 April 2012
Problem
The area of the largest triangle that can be inscribed in a semi-circle whose radius is is:
Solution
The area of a triangle is To maximize the base, let it be equal to the diameter of the semi circle, which is equal to
To maximize the height, or altitude, choose the point directly in the middle of the arc connecting the endpoints of the diameter. It is equal to
Therefore the area is
See Also
1950 AHSME (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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |