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
_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95

UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".