The number of diagonals in a polygon, $d$, in terms of the number of sides of a polygon, $n$, is given by the equation $d=\frac{n(n-3)}{2}$.

What equation shows the number of sides of a polygon in terms of the number of diagonals
A. $n=\sqrt{\frac{2 d}{3}}$
B. $n=\sqrt{2 d+3}$
c. $n=\sqrt{2 d}+3$
D. $n=\sqrt{2 d+\frac{9}{4}}+\frac{3}{2}$

Answer

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Answer

The final answer is: $\boxed{n=\sqrt{2d+\frac{9}{4}}+\frac{3}{2}}$

Steps

Step 1 ：Given the equation for the number of diagonals in terms of the number of sides: $d=\frac{n(n-3)}{2}$

Step 2 ：Solve for n using the quadratic formula: $n = \frac{3 \pm \sqrt{9 + 8d}}{2}$

Step 3 ：The final answer is: $\boxed{n=\sqrt{2d+\frac{9}{4}}+\frac{3}{2}}$