2006 Cyprus MO/Lyceum/Problem 21

Problem

A convex polygon has $n$ sides and $740$ diagonals. Then $n$ equals

A. $30$

B. $40$

C. $50$

D. $60$

E. None of these

Solution

The number of diagonals is $\frac{n(n-3)}{2} = 740 \Longrightarrow n(n-3) = 1480$ . By either solving the quadratic equation or by substituting the answer choices, we get $n = 40 \Longrightarrow \mathrm{B}$ .

2006 Cyprus MO, Lyceum (Problems)
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2006 Cyprus MO/Lyceum/Problem 21

Problem

Solution

See also