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The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle? Express your answer in terms of pi and simplest radical form.

 Aug 13, 2018
 #1
avatar+15105 
+3

The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle?

 

perimeter = 3a

radius O = r

 

cos(30°)=a2rr=a2cos(30°)a=2rcos(30°)

 

3a=r2π

 

3a=(a2cos(30°))2π3a=πa24cos2(30°)a=34cos2(30°)π=34(123)2π=32πa=2.86479..

 

r=34cos2(30°)2πcos(30°)r=6cos(30°)π=6(123)π=33πr=1.65399

 

proof:
 

perimeter=area O3a=r2π334cos2(30°)π=π(6cos(30°)π)28.59437=8.59437

 

laugh  !

 Aug 13, 2018
edited by asinus  Aug 13, 2018
edited by asinus  Aug 14, 2018
edited by asinus  Aug 14, 2018
edited by asinus  Aug 14, 2018
 #2
avatar+12530 
+4

The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle? Express your answer in terms of pi and simplest radical form.

laugh

 Aug 13, 2018

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