BN1989 wrote:

An equilateral triangle is inscribed in a circle. If the perimeter of the triangle is z inches and the area of the circle is y square inches, which of the following equations must be true?

A) \(9z^2-\pi y=0\)

B) \(3z^2-\pi y=0\)

C) \(\pi z^2-3y=0\)

D) \(\pi z^2-9y=0\)

E) \(\pi z^2-27y=0\)

Perimeter of equilateral triangle = z

So, side of equilateral triangle = z/3

Median of equilateral triangle = \(\frac{\sqrt{3}}{2} * (z/3)\)

Radius of circle = 2/3 * Median of equilateral triangle = 2/3 * \(\frac{\sqrt{3}}{2} * (z/3)\) = \(\frac{z}{3 \sqrt{3}}\)

Area of circle = y = \(\pi {\frac{z}{3 \sqrt{3}}}^2\) = \(\pi \frac{z^2}{27}\)

27y = \(\pi {z^2}\)

\(\pi z^2-27y=0\)

Answer E
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