Search any question & find its solution
Question:
Answered & Verified by Expert
If a polygon of $n$ sides has 275 diagonals, then $n$ is equal to
Options:
Solution:
1494 Upvotes
Verified Answer
The correct answer is:
$25$
A polygon of $n$ sides has number of diagonals
$=\frac{n(n-3)}{2}=275 \quad$ (given)
$\begin{array}{cc}\Rightarrow & n^2-3 n-550=0 \\ \Rightarrow & n^2-25 n+22 n-550=0 \\ \Rightarrow & n(n-25)+22(n-25)=0 \\ \Rightarrow & (n-25)(n+22)=0 \\ \Rightarrow & n=25,(\because n=-22 \text { is not possible })\end{array}$
$=\frac{n(n-3)}{2}=275 \quad$ (given)
$\begin{array}{cc}\Rightarrow & n^2-3 n-550=0 \\ \Rightarrow & n^2-25 n+22 n-550=0 \\ \Rightarrow & n(n-25)+22(n-25)=0 \\ \Rightarrow & (n-25)(n+22)=0 \\ \Rightarrow & n=25,(\because n=-22 \text { is not possible })\end{array}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.