BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

In the above diagram,

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

In the above diagram,

by Brent@GMATPrepNow » Thu Apr 09, 2020 7:25 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Image

In the above diagram, ∠QPT = ∠RST = 30°. If the area of triangle PTS = √12, what is the area of square PQRS?

A) 3√3
B) 6
C) 8
D) 6√2
E) 4√3

Answer: C
Source: www.gmatprepnow.com
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Re: In the above diagram,

by Brent@GMATPrepNow » Fri Apr 10, 2020 5:19 am
Brent@GMATPrepNow wrote: ↑
Thu Apr 09, 2020 7:25 am
 Image

In the above diagram, ∠QPT = ∠RST = 30°. If the area of triangle PTS = √12, what is the area of square PQRS?

A) 3√3
B) 6
C) 8
D) 6√2
E) 4√3

Answer: C
Source: www.gmatprepnow.com
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:
Image

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1