Last visit was: 27 Apr 2024, 07:57 It is currently 27 Apr 2024, 07:57

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 28658
Own Kudos [?]: 33140 [2]
Given Kudos: 25178
Send PM
avatar
Intern
Intern
Joined: 14 Jun 2018
Posts: 36
Own Kudos [?]: 13 [0]
Given Kudos: 0
Send PM
avatar
Retired Moderator
Joined: 20 Apr 2016
Posts: 1307
Own Kudos [?]: 2214 [0]
Given Kudos: 251
WE:Engineering (Energy and Utilities)
Send PM
Intern
Intern
Joined: 26 Dec 2023
Posts: 44
Own Kudos [?]: 14 [0]
Given Kudos: 4
Send PM
Re: If PQ = 1, what is the length of RS [#permalink]
pranab223 wrote:
Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project

[/url]



If \(PQ = 1\), what is the length of \(RS\)
A. \(\frac{1}{12}\)

B. \(\frac{\sqrt{3}}{12}\)

C. \(\frac{1}{6}\)

D. \(\frac{2}{3 \sqrt{3}}\)

E. \(\frac{2}{\sqrt{12}}\)



Here PQ = 1

Plz see the diagram attached.

Now △ PQT,

∠QPT = 30° , ∠QTP = 90° and ∠PQT = 60°


so it is a 30° - 60° -90° and we know the sides are distributed in the ratio \(1 : \sqrt3 : 2\)

Now PQ = 1,
so \(QT = \frac{1}{2} and PT = \frac{2}{sqrt3}\)

Now let us consider △ QTS


∠TQS = 30° , ∠QST = 60° and ∠QTS = 90°

so it is a 30° - 60° -90° and we know the sides are distributed in the ratio \(1 : \sqrt3 : 2\)

Now \(QT = \frac{1}{2}\),
so \(QS = \frac{1}{\sqrt3} and TS = \frac{1}{2\sqrt3}\)

Now let us consider △ TRS


∠RST = 60° , ∠RTS = 30° and ∠TRS = 90°

so it is a 30° - 60° -90° and we know the sides are distributed in the ratio \(1 : \sqrt3 : 2\)

Now \(TS = \frac{1}{2\sqrt3}\),
so \(RT = \frac{1}{4} and RS = \frac{1}{4\sqrt3}\).

But \(RS = \frac{1}{4\sqrt3}\) can also be written as \(RS = \frac{1}{4\sqrt3} *\frac{\sqrt3}{\sqrt3} = \frac{\sqrt3}{12}\)



Is it not PT = Sqrt(3)/2? If it is 2/sqrt(3), what am I doing wrong to get sqrt(3)/2?
Prep Club for GRE Bot
[#permalink]
Moderators:
Moderator
1085 posts
GRE Instructor
218 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne