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Polygons | Polygons Exercise 14B

Question 3

A polygon has 27 diagonals. How many sides does it have?

(a) 7 (b) 8 (c) 9 (d) 12

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(c) 9

Explanation:

We know that to calculate number of diagonals in octagon is

Number of diagonals is= n × (n -3)/2

27= n × (n -3)/2

n (n-3) = 54

n2- 3n = 54

n2- 3n-54 = 0

(n + 6) (n - 9)=0

n=-6 or n=9

So that we are calculating the sides it should be positive, therefore sides of the polygon have 27

diagonals are 9

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Question 3

A polygon has 27 diagonals. How many sides does it have?

(a) 7 (b) 8 (c) 9 (d) 12

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

(c) 9

Explanation:

We know that to calculate number of diagonals in octagon is

Number of diagonals is= n × (n -3)/2

27= n × (n -3)/2

n (n-3) = 54

n2- 3n = 54

n2- 3n-54 = 0

(n + 6) (n - 9)=0

n=-6 or n=9

So that we are calculating the sides it should be positive, therefore sides of the polygon have 27

diagonals are 9

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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