Solve.
-The equation $D = \frac { 1 } { 2 } n ( n - 3 )$ gives the number of diagonals $D$ for a polygon with $n$ sides. Find the number of sides $\mathrm { n }$ for a polygon that has 54 diagonals.

Question

Quizplus · Accepted Answer

To find the number of sides $n$, set $D = 54$ and solve the equation: $54 = \frac{1}{2}n(n-3)$. Multiply both sides by 2 to get $108 = n(n-3)$. This simplifies to $n^2 - 3n - 108 = 0$. Solving this quadratic equation using the quadratic formula or factoring gives $n = 12$.

Solve -The Equation D=12n(n−3)D = \frac { 1 } { 2 } n ( n - 3 )D=21​n(n−3)

Solve
-The Equation $D = \frac { 1 } { 2 } n ( n - 3 )$