Figure shows a sector of a circle of radius r containing an angle `theta^@` The area of the sector is `A cm^2` and the perimeter is 50cm. Prove that `theta = (360)/pi ((25)/r-1)` and `A=25r -r^2`

Explanation

Perimeter of the sector =50cm

r is radius of a sector and `theta` is angle of the sector.

Perimeter of the sector =
`((theta)/(360^0) xx 2pir)+2r`

`:. 50 = ((theta)/(360^0) xx 2pir)+2r`

`:. 50 - 2r = (theta)/(360^0) xx 2pir`

`:. 2 (25- r) = (theta)/(360^0) xx 2pir`

`:. theta =( (25-r) xx 360^0)/(pir)`

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