Question

The number of diagonals in a polygon is 14. How many sides does the polygon have ?​

Answer 1

hey there

here is your answer

we know that ,

diagonals of a polygon with side  n  = n(n - 3 ) / 2

given that the polygon has 14 diagonals

n ( n - 3 ) = 14 * 2

transposing 2

n² - 3n - 28 = 0

solve the equation using splitting the middle term

-7 * 4 = -28

-7 + 4 = -3

therefore

n² - 7n + 3n - 28

n ( n - 7 ) + 3 ( n - 7 )

( n + 3) ( n - 7 ) =  0

therefore

n = 7 or n = -3

but the number of sides of a polygon cant be negative

therefore the polygon has 7 sides  

hope it helps you

please mark as brainliest

Answer 2

Answer:

7 sides

Step-by-step explanation:

Number of diagonals = 14

Let the Number of sides be n

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

14 = (n^2 - 3n)/2

28 = n^2 - 3n

n^2 - 3n - 28 = 0

n^2 + 4n - 7n - 28 = 0

n(n + 4) - 7(n + 4) =0

(n - 7)(n + 4) = 0

Since, the product is 0.

Therefore, at least one of the factors is 0.

n - 7 = 0

n = 7

OR

n + 4 = 0

n = -4

Since, a polygon can't have negative sides.

Therefore, the answer is 7.