GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
An equilateral triangle is inscribed in a circle. If the perimeter of
[#permalink]
06 Sep 2021, 10:00
06 Sep 2021, 10:00
1
Expert Reply
2
Bookmarks
00:00
Question Stats:
81% (02:40) correct
18% (02:06) wrong based on 16 sessions
Hide Show timer Statistics
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) \(\pi z^2-27y=0\)
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) \(\pi z^2-27y=0\)
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
An equilateral triangle is inscribed in a circle. If the perimeter of
[#permalink]
30 Nov 2021, 06:25
30 Nov 2021, 06:25
3
Attachment:
temp-2.JPG [ 30.92 KiB | Viewed 2290 times ]
Side of an equilateral triangle (a) inscribed in a circle with radius r is given by a = rโ๐
[ Watch this video to know how ]
=> Perimeter of triangle = 3a = 3 * โ๐ r = z (given) => r = \(\frac{z }{ 3 โ๐}\)
Area of circle with radius r = \(\pi r^2\) = y (given)
=> \(\pi\) * \((\frac{z }{ 3 โ๐})^2\) = y (substituting value of r from (1) )
=> \(\pi\) * \(\frac{z^2}{9*3}\) = y
=> \(\pi\) * \(\frac{z^2}{27}\) = y
=> \(\pi\) * \(z^2\) = 27 * y
=> \(\pi z^2-27y=0\)
So, Answer will be E
Hope it helps!
Watch the following video to Learn Properties of Equilateral Triangle inscribed in a Circle
General Discussion
Re: An equilateral triangle is inscribed in a circle. If the perimeter of
[#permalink]
06 Sep 2021, 17:42
06 Sep 2021, 17:42
3
Answer is E) pi *z^2โ27y=0
Let s be the side of the triangle and r be the radius of the circle, the relation between them is s = r * sqrt(3).
So z = 3 * s = 3*sqrt(3) * r.
and area = pi * r^2.
All the answer choices are relation between y and z and y already has a pi in it, so in the answer only C,D,E has pi multiplied for z.
Next step is simple, relation between z and y in terms of r and E is the only one that satisfies.
PS: Not sure this is the GRE method, please share if there is a shorter approach.
Let s be the side of the triangle and r be the radius of the circle, the relation between them is s = r * sqrt(3).
So z = 3 * s = 3*sqrt(3) * r.
and area = pi * r^2.
All the answer choices are relation between y and z and y already has a pi in it, so in the answer only C,D,E has pi multiplied for z.
Next step is simple, relation between z and y in terms of r and E is the only one that satisfies.
PS: Not sure this is the GRE method, please share if there is a shorter approach.
