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# The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius, the angle of the sector is A. 65o 24' B. 64o 24' C. 63o 24' D. 62o 24

SHAIK AASIF AHAMED
6 years ago
Hello student,
perimeter of sector = 2$\pi$rA/360 + 2r
Here, A = angle of sector
And, length of arc of semi-circle of same radius = $\pi$r
Thus,
$\pi$rA/180 + 2r = $\pi$r
On solving,
A = 180(1 - 2/$\pi$) taking $\pi$= 22/7
We get, A = 720/11
Hence A is the correct answer
Thanks and Regards
shaik Aasif