## anonymous one year ago The diagram shows the aerial view of a park. What is the length of the park's boundary to the nearest yard? Use the value π = 3.14. 215 yards 266 yards 285 yards 309 yards http://cdn.ple.platoweb.com/PCAP-ASSETS-PROD/6ba968e838ff470d8f9f18b417492d85

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1. anonymous

assuming that the limits are the perimeter of this park: |dw:1436148213050:dw| and for the left and right $L=\theta*R$ theta is in rad $\frac{ 120 \pi }{ 180 } = \frac{ 2 \pi }{ 3 }$ $L= \frac{ 2 \pi }{ 3 }*50=104.7$ calculating the perimeter: $2*50+2*104.7=309.4$ I think that the answer is 309

2. mathstudent55

@baad1994 You are correct. You can also use the formula $$s = \dfrac{x}{360^o} \times 2 \pi r$$ for the length of an arc and avoid having to convert to radians. $$P = 2 \times \left( \dfrac{120}{360}\times 2 \pi \times 50 ~yd \right) + 2 \times 50~yd = 309 ~yd$$