Difference between revisions of "1957 AHSME Problems/Problem 7"
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Revision as of 12:20, 12 October 2020
Problem 7
The area of a circle inscribed in an equilateral triangle is . The perimeter of this triangle is:
Solution
We can see that the radius of the circle is
. We know that the radius is
of each median line of the triangle; each median line is therefore
. Since the median line completes a
-
-
triangle, we can conclude that one of the sides of the triangle is
. Triple the side length and we get our answer,
.
See Also
1957 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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 |
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