IMO C
h=a*(sqrt3)/2;a=side;h=height
4*sqrt(3)=a*sqrt(3)/2
a=8
perimeter=3*8=24
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
GMATprep: geometry
Source: Beat The GMAT — Problem Solving |
The answer is C
But the solution is much easier.
When we have a right triangle with one side equal x*3/2 the ather side is equal to x, and the hipotenuse 2x - so PS = 4, PQ = 8 - perimeter is 24
But the solution is much easier.
When we have a right triangle with one side equal x*3/2 the ather side is equal to x, and the hipotenuse 2x - so PS = 4, PQ = 8 - perimeter is 24
-
briantime
- Junior | Next Rank: 30 Posts
- Posts: 13
- Location: Baden-Baden, Germany
- Thanked: 2 times
- GMAT Score:690
Since we have an equilateral triangle, the angles are all equal (60°).In the figure shown, the length of line segment QS is 4 sqrt(3). What is the perimeter of equilateral triangle PQR?
- 12
- 12 sqrt(3)
- 24
- 24 sqrt(3)
- 48
Angle QPS = 60
Angle QSP = 90
Therefore, PQS = 180 - 60 - 90 = 30 OR PQS = 1/2 * PQR = 1/2 * 60 = 30
In a 30° - 60° - 90° triangle, the sides have length ratios of 1 : sqrt(3) : 2.
Therefore, the ratios of our triangle are 4 : 4 sqrt(3) : 8.
2*4 + 2*8 = 24
Since this is an equilateral triangle we know that the length of PS = 1/2 the length of PQ. Let's call the length of PQ a.
By Pythagorean Theorem then we know that
PQ^2 = PS^2 + QS^2
Substituting in a for PQ, a/2 for PS and 4 sqrt 3 for QS we get
a^2 = (a/2)^2 + (4 sqrt 3)^2
or
a^2 = (a^2)/4 + 48
solving for a^2
a^2 = 64
or
a = 8
The perimeter of the triangle is thus 3a or 3 times the length of PQ or 24
By Pythagorean Theorem then we know that
PQ^2 = PS^2 + QS^2
Substituting in a for PQ, a/2 for PS and 4 sqrt 3 for QS we get
a^2 = (a/2)^2 + (4 sqrt 3)^2
or
a^2 = (a^2)/4 + 48
solving for a^2
a^2 = 64
or
a = 8
The perimeter of the triangle is thus 3a or 3 times the length of PQ or 24
jdd147 wrote:Since this is an equilateral triangle we know that the length of PS = 1/2 the length of PQ. Let's call the length of PQ a.
By Pythagorean Theorem then we know that
PQ^2 = PS^2 + QS^2
Substituting in a for PQ, a/2 for PS and 4 sqrt 3 for QS we get
a^2 = (a/2)^2 + (4 sqrt 3)^2
or
a^2 = (a^2)/4 + 48
solving for a^2
a^2 = 64
or
a = 8
The perimeter of the triangle is thus 3a or 3 times the length of PQ or 24
What am i doing wrong here ?
PQ^2 = QS^2 + PS^2
PQ^2 = PS^2 + 48 ------ (1)
QR^2 = SR^2 + 48 ------(2)
Adding 1 and 2
PQ^2 + QR^2 = PS^2 + SR ^2 + 96 ----- 3
But, PS^2 + SR ^2 = PR ^2 ------- 4
Substitute 4 in 3....
PQ^2 + QR^2 = PR^2 + 96 -----5
PQ = PR = QR since equilateral triangle
Therefore PQ^2 = 96
PQ = sqrt (96)
But this doesnt yield the correct answer ....
