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.
Jun 24Get an Extra 30% Off Target Test Prep Plans
12:00 PM EDT
-11:59 PM EDT
Get 30% off any Target Test Prep GRE plan during our Flash Sale. Just enter the coupon code FLASH30 at checkout to save big. Hurry up and grab the offer before it's too late!
Jun 24TTP Student Brian Scored 338 (Q169/V169) on the GRE
01:00 PM EDT
-11:59 PM EDT
Join Brian and many other students who have used Target Test Prep to score high on the GRE. Grab a 30% discount before it’s too late, or try before you buy with a 5-day, full-access trial of the course for FREE
Jul 09Sign up for 1 Week GRE Free Trial
10:00 AM PDT
-11:00 AM PDT
Free 1-week access to over 20 lesson videos and 20 practice questions. No payment info required.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS
[#permalink]
09 Apr 2020, 07:24
09 Apr 2020, 07:24
2
2
Bookmarks
00:00
Question Stats:
82% (01:29) correct
17% (02:27) wrong based on 29 sessions
Hide Show timer Statistics
In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS = √12, what is the area of square PQRS?
A) 3√3
B) 6
C) 8
D) 6√2
E) 4√3
Intern
Joined: 30 Mar 2020
Posts: 27
Given Kudos: 0
WE:Research (Health Care)
Re: In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS
[#permalink]
10 Apr 2020, 00:19
10 Apr 2020, 00:19
1
Answer: 8
Triangle PTS is an equilateral triangle.
Lets split triangle PTS into x:x√3:2x
PS=X
PS/2=X/2
X√3=x√3/2
√12=X*√3/2 *1/2
√12=X2√3/4
4√12=X2√3
4√3√4=X2√3
4√4=X2
8=X2
√8=X
Area of Square: PS * QP = √8 * √8 = 8
Triangle PTS is an equilateral triangle.
Lets split triangle PTS into x:x√3:2x
PS=X
PS/2=X/2
X√3=x√3/2
√12=X*√3/2 *1/2
√12=X2√3/4
4√12=X2√3
4√3√4=X2√3
4√4=X2
8=X2
√8=X
Area of Square: PS * QP = √8 * √8 = 8
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS
[#permalink]
10 Apr 2020, 05:13
10 Apr 2020, 05:13
1
GreenlightTestPrep wrote:
In the above diagram, ∠QPT = ∠RST = 30°. If the area of ∆PTS = √12, what is the area of square PQRS?
A) 3√3
B) 6
C) 8
D) 6√2
E) 4√3
Since we're told PQRS is a SQUARE, we know that all 4 angles are 90 degrees.
So, if ∠QPT = ∠RST = 30°, then the two other angles are each 60°
If two of the angles in the triangle 60° each, then the third angle must also be 60° [since angles in a triangle add to 180°]
So, we now know that triangle PTS is an equilateral triangle
We get:
Area of equilateral triangle [(√3)/4](side²)
Since we're told the area of ∆PTS = √12, we can write: [(√3)/4](x²)=√12
Multiply both sides by 4 to get: (√3)(x²)=4√12
Divide both sides by √3 to get: x² = (4√12)/(√3)
Simplify numerator: x² = (8√3)/(√3)
Simplify : x² = 8
Since the area of square PQRS = x², we know that the area of square PQRS is 8
Answer: C
Cheers,
Brent
