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The vertices of an equilateral triangle, with perimeter P and area A, lie on a circle with radius r. Find an expression for P/A in terms of r.

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sqdancefan

Answer:

  4/r

Step-by-step explanation:

The side lengths s of an equilateral triangle inscribed in a circle of radius r will be ...

  s = r√3

The perimeter of the triangle will be 3s.

The area of the triangle will be s^2·(√3)/4.

Then the ratio P/A is ...

  P/A = (3s)/(s^2·(√3)/4) = (4√3)/s

Substituting the above expression for s, we have ...

  P/A = 4√3/(r√3)

  P/A = 4/r

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