An equilateral triangle is inscribed in a circle of radius r. See the figure. Express the circumference C of the circle as a function of the length x of a side of the triangle.
[Hint: First show that r^2 = x^2/3.]

Question

An equilateral triangle is inscribed in a circle of radius r. See the figure. Express the circumference C of the circle as a function of the length x of a side of the triangle.
[Hint: First show that r^2 = x^2/3.]

akashdeepdeb · Answer

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anonymous · Answer

x is = to (square root of 3) * r

akashdeepdeb · Answer

If you found that out from trigonometry then good job!

Okay, so x = $\sqrt{3} r$
What is r = ?

$$r =\frac{x}{\sqrt{3}}$$
$$C = 2 \pi ~(r)~$$
$$C = 2 \pi ~(\frac{x}{\sqrt{3}})$$
$$C = \frac{2}{\sqrt{3}} \pi x$$
$$C(x) = \frac{2}{\sqrt{3}} \pi x$$

Hence, you have successfully shown C as a function of x (which IS the side of the equilateral triangle).

Understood? :)