A polygon has prime number of sides. If the number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is

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Solution

The correct option is B
5

The least consecutive primes are 2 and 3.
$∴$ number of sides = 2 + 3 = 5
The number of diagonals in a polygon = $\frac{n (n - 3)}{2}$
Here $n = 5.$
Therefore, the number of diagonals in a pentagon = $\frac{5 (5 - 3)}{2}$ = 5.

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Q. A polygon has prime number of sides. If number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is

Question 13
A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is
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A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is
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Q. Assertion :If a polygon has

35

diagonals then the number of the sides of the polygon is

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. Reason: The number of diagonals of polygon with

n

sides is

\frac{n (n - 3)}{2}

Q. A polygon of n sides has

\frac{n (n - 3)}{2}

diagonals. If a polygon has 9 diagonals, find the number of sides of the polygon.

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A polygon has prime number of sides. If the number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is

The correct option is B 5 The least consecutive primes are 2 and 3. ∴ number of sides = 2 + 3 = 5 The number of diagonals in a polygon = n(n−3)2 Here n=5. Therefore, the number of diagonals in a pentagon = 5(5−3)2 = 5.

The correct option is B
5

The least consecutive primes are 2 and 3.
$∴$ number of sides = 2 + 3 = 5
The number of diagonals in a polygon = $\frac{n (n - 3)}{2}$
Here $n = 5.$
Therefore, the number of diagonals in a pentagon = $\frac{5 (5 - 3)}{2}$ = 5.