Matilda is planning a walk around the perimeter of wedge park, which is shaped like a circular wedge, as shown below. the walk around the park is 2.9 miles, and the park has an area of 0.25 square miles. if θ is less than 90 degrees, what is the value of the radius, r? (round your answer to two decimal places.) mi

The area of the circular sector is


From that, the equation for the central angle is


The perimeter of the circular sector is the sum of the arc length and twice the radius.


From that, the equation for the central angle is


The value of r can be found by equating these two expressions for θ.


By any of several means, you can find that r=0.2 or 1.25. The latter value corresponds to the requirement that the central angle be less than 90°. The radius is ...
  1.25 miles.

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