Question

Assertion :If a polygon has $35$ diagonals then the number of the sides of the polygon is $15$. Reason: The number of diagonals of polygon with $n$ sides is $\frac{n(n-3)}{2}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect and Reason is correct

Answer 1

The correct option is D Assertion is incorrect and Reason is correct

Each diagonal connects one point to another point in the polygon that isn’t its next-door neighbor. In an n-sided polygon, you have n starting points for diagonals. And each diagonal can go to (n-3) ending points because a diagonal can’t end at its own starting point or at either of the two neighboring points. So the first step is to multiply n by (n-3).

Then , because each diagonal’s ending point can be used as a starting point as well, the product n (n-3) counts each diagonal twice. That’s why you divide by 2.

number of diagonals= $\frac{n\times (n-3)}{2}$

For a polygon having 35 diagonals, no of sides would be

$n^2-3n=2\times 35⟹n^2-3n-70=0⟹n=10\ne 15$

Reason is correct but assertion is wrong