Question

if a polygon has 20 diagonals. Find the number of sides​

Answer 1

Answer:

Given:

Number of diagonals of a polygon = 20

To find:

The number of sides of the polygon

Calculation:

The number of diagonals of a polygon having n sides is given by the formula

Number of diagonals = n(n-3)/2

By substituting the given data in the above

formula

=> Number of diagonals = n(n-3)/2

=> 20 = n(n-3)/2 => 40 = n²-3n

=> n²-3n-40 = 0

=> n²-8n+5n-40 = 0

=> n(n-8)+5(n-8) = 0

=> (n-8)(n+5) = 0

As n cannot be negative

=> n-8 = 0

=> n = 8

The number of sides of the polygon are 8

Step-by-step explanation:

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Answer 2

Given :-

• Number of diagonals of a polygon = 20

To find :-

• The number of sides of the polygon

Calculation :-

The number of diagonals of a polygon having n sides is given by the formula

Number of diagonals = n(n-3)/2

By substituting the given data in the above  formula

=> Number of diagonals = n(n-3)/2

=> 20 = n(n-3)/2 => 40 = n²-3n

=> n²-3n-40 = 0

=> n²-8n+5n-40 = 0

=> n(n-8)+5(n-8) = 0

=> (n-8)(n+5) = 0

As n cannot be negative

=> n-8 = 0

=> n = 8

The number of sides of the polygon are 8