Question

2.Given that the perimeter of the sector AOB is 18 cm and that the area
is 8cm 2 calculate the value r and Θ.

Show proper working

Answer 1

Answer:-

The arc length s = rθ

perimeter of sector = 2r + s = 2r+rθ

2r + rθ = 18

θ = 18/r - 2

area of sector = πr²·θ/(2π) = r²θ/2

r²θ/2 = 8

r²θ = 16

substitution

r²(18/r - 2) = 16

2r² - 18r + 16 = 0

r = 8,1

1 is an extraneous solution, so r = 8.

s = 18-2r = 2

θ = s/r = 0.25 radian

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