Question

Find the perimeter of a triangle inscribed in a circle with radius of 3 inches

Answer 1

An equilateral triangle is inscribed in a circle.







A

B

C

D

E

DIFFICULTY:

     75% (hard)

QUESTION STATS:

 based on 239 sessions

62% (02:38) correct

38% (04:36) wrong

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) 9z2−πy=09z2−πy=0

B) 3z2−πy=03z2−πy=0

C) πz2−3y=0πz2−3y=0

D) πz2−9y=0πz2−9y=0

E) πz2−27y=0πz2−27y=0

[Reveal] Spoiler: OA

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Bunuel

EXPERT'S 
POST

Apr 11, 2012

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) 9z²-pi*y=0
B) 3z²-pi*y=0
C) pi*z²-3y=0
D) pi*z²-9y=0
E) pi*z²-27y=0

We need to establish a relationship between the perimeter of the triangle and the area of the circle.

The radius of the circumscribed circle is R=a3√3R=a33, where aa is the side of the inscribed equilateral triangle (check this for more: math-triangles-87197.html).

Now, the area of the circle is πr2=πa23=yπr2=πa23=y and the perimeter of the triangle is 3a=z3a=z. Now, you can plug these values in answer choices to see which is correct.

Option E fits: πz2−27y=9a2π−9a2π=0πz2−27y=9a2π−9a2π=0.

Answer: E.