Question

Assertion :Perimeter of a regular pentagon inscribed in a circle with centre $O$ and radius $a$cm equals $10a\sin {36}^0$cm. Reason: Perimeter of a regular polygon inscribed in a circle with centre $O$ and radius $a$ cm equals $(3n-5)\sin \left(\frac{{360}^0}{n}\right)$cm, then it is $n$ sided, where $n\ge 3$

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

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

$\because \angle A_{1}O{A}_2=\frac{2\pi }{n}$
$\therefore \angle A_{1}OM=\angle A_{2}OM=\frac{\pi }{n}$
$\therefore A_1{A}_2=2M{A}_2$
$=2a\sin \left(\frac{\pi }{n}\right)$cm
$\therefore$Perimeter$=2an\sin \left(\frac{2\pi }{2n}\right)$cm
$=2an\sin \left(\frac{{360}^0}{2n}\right)$cm
For $n=5$
Perimeter is $10a\sin \left(\frac{{360}^0}{2\times 5}\right)=10a\sin {36}^0$cm