Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 21"
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A convex polygon has <math>n</math> sides and <math>740</math> diagonals. Then <math>n</math> equals | A convex polygon has <math>n</math> sides and <math>740</math> diagonals. Then <math>n</math> equals | ||
− | + | <math>\mathrm{(A)}\ 30\qquad\mathrm{(B)}\ 40\qquad\mathrm{(C)}\ 50\qquad\mathrm{(D)}\ 60\qquad\mathrm{(E)}\ \text{None of these}</math> | |
− | + | ==Solution== | |
+ | The number of diagonals in a polygon is <math>\frac{n(n-3)}{2}</math>. In this case, <math>\frac{n(n-3)}{2}=740</math>, so <math>n(n-3)=1480</math>. | ||
− | + | By solving the [[quadratic equation]], we find <math>n = 40</math>, so the answer is <math>\mathrm{B}</math>. | |
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==See also== | ==See also== |
Revision as of 13:21, 26 April 2008
Problem
A convex polygon has sides and
diagonals. Then
equals
Solution
The number of diagonals in a polygon is . In this case,
, so
.
By solving the quadratic equation, we find , so the answer is
.
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 21 |
Followed by Problem 22 | |
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 |