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Figure 1 shows a sector AOB of a circle with centre O and radius r cm. The angle AOB is θ radians. The area of the sector AOB is 11 cm2 Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r.

theta/2pi x2pir = length of ABso therefore simplifying gives... thetar = AB
Perimeter = 2r+thetarequate the answer of 4AB to the perimeter.Solve for theta which eventually give 2/3then put theta in the equation for the area of the sector which equals 11cm^2then solve for rthe answer should be the positive square root of 33

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Figure 1 shows a sector AOB of a circle with centre O and radius r cm. The angle AOB is θ radians. The area of the sector AOB is 11 cm2 Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r.

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