Question

A polygon has 20 diagonals. The number of sides is:​

Answer 1

$\Large\underline\mathfrak{Question}$

$\red{\textbf{A polygon has 20 diagonals.}} \\ \textbf{The number of sides is ?}$

$\Large\bold\star\underline{\underline\textbf{Formula\:used}}$

$\pink{\large\boxed{\boxed{\bold{ \frac{n(n - 3)}{2} }}}}$

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$\bold{\boxed{\large{\boxed{\orange{\small{\boxed{\large{\red{\bold{\:Answer}}}}}}}}}}$

$\red\longmapsto\:\rm \green{\dfrac{n(n - 3)}{2} = 20} \\ \\ \red\longmapsto\:\rm \: \blue{n(n - 3) = 20 \times 2} \\ \\ \red\longmapsto\orange{\rm \: {n}^{2} - 3n - 40 = 0} \\ \\\red\longmapsto\:\rm \: {n}^{2} - 8n + 5n - 40 = 0 \\ \\ \red\longmapsto\:\rm \red{n(n - 8) + 5(n - 8) = 0} \\ \\ \red\longmapsto\:\rm \purple{(n - 8)(n + 5) = 0} \\ \\ \red\longmapsto\:\bf \: n = 8 \: or \: ( - 5) \\ \\ \red\longmapsto\: \large\underline{\boxed{\bf\green{n} \orange= \purple8}}$

$\blue{\underline\textbf{Hence, The Polygon Have 8 sides.}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \huge\bold{\red{\ddot{\smile}}}$

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Answer 2

$\huge{\mathfrak{Bonjour!♡}}$•°⭑

$\bullet\underline{\textsf{\color{grey}{AnsWer:-}}}$

→8 sides

$\bullet\underline{\textsf{\color{grey}{SteP By SteP ExplainaTion:-}}}$

The diagonal of a polygon is given by the formula;

$\longrightarrow \: { \tt{ \frac{n(n - 3)}{2} = 20}} \\ \\ \rightarrow \:{ \tt{ n {}^{2} - 3n = 40}} \\ \\ \rightarrow \:{ \tt{ n { }^{2} - 3n - 40 = 0}} \\ \\ \rightarrow{ \tt{(n - 8)(n + 5) = 0}} \\ \\ \rightarrow \: { \bf{n = 8 \: or \: - 5}}$

But the number of side must be positive;

•°• The number of side of the polygon = 8.