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Question

The perimeter of a sector of a circle is the sum of the two sides formed by the radii and the length of the included arc. A sector of a particular circle has a perimeter of 28 cm and an area of 49 sq cm. What is the length of the arc of this sector?

Accepted Answer

Let the length of the arc of this sector be s cm and the radius of the circle be r cm. Then this sector is s/2 r of a full circle, and its area is s2 r r^2 = rs2 = 49 square cm. Also, we compute the sector's perimeter to be 2r + s = 28 cm. Solving, we find that s = 14 cm.