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Triangle ABC is equilateral with side length 3. A point x is randomly chosen within ABC . What is the probability that X is no more than 1 unit away from vertex A?

Lightning  Mar 29, 2018
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The area  of  the triangle  is

(1/2) (3)^2 √3/2  =  (9/4)√3  units^2

 

The  area  that is no more than  unit from A  is (1/6) of a circle with a center at A and a radius of 1 =

 

pi *(1/6)(1)^2   =   pi / 6  units' 2

 

So....the probability  that X  is no more than 1 unit from A  is

 

[pi / 6 ]   /  [(9/4)√3 ]  =

 

4 pi  / [ 54√3]  =

 

2pi / [27√3 ]  ≈  0.134  ≈   13.4 %

 

 

cool cool cool

CPhill  Mar 29, 2018

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