The formula $D = \frac { n ( n - 3 ) } { 2 }$ yields the number of diagonals, D , in a polygon of n sides. Find the number of sides of a polygon that has 35 diagonals.
A) 11 sides
B) 12 sides
C) 8 sides
D) 10 sides
E) 9 sides

Question

Quizplus · Accepted Answer

We can use the given formula and solve for n:
\begin{align*}
D &= \frac{n(n-3)}{2}\
35 &= \frac{n(n-3)}{2}\
70 &= n(n-3) \
0 &= n^2 - 3n - 70 \
0 &= (n-10)(n+7) \
\end{align*}
Since we are dealing with the number of sides of a polygon, we can safely ignore the negative solution $n=-7$. Thus, the only valid solution is $n=10$, so the polygon has 10 sides. Therefore, the answer is D) 10 sides.

The Formula D=n(n−3)2D = \frac { n ( n - 3 ) } { 2 }D=2n(n−3)​

The Formula $D = \frac { n ( n - 3 ) } { 2 }$