Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 23 Jul 2019, 07:33

### GMAT 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

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

Practice
Pays

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

# Is the area of equilateral triangle E less than the area of square C ?

Author Message
TAGS:

### Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 530
GPA: 2.81
Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

### Show Tags

05 Jun 2016, 14:19
1
00:00

Difficulty:

55% (hard)

Question Stats:

66% (01:45) correct 34% (02:02) wrong based on 102 sessions

### HideShow timer Statistics

Is the area of equilateral triangle E less than the area of square C ?

(1) A side of square C is $$\frac{2}{3}$$ the length of a side of triangle E.

(2) The sum of the perimeters of triangle E and square C is 17

_________________
Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges
Retired Moderator
Joined: 13 Apr 2015
Posts: 1676
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

### Show Tags

06 Jun 2016, 03:59
Let 'l' be the length of square and 'a' be the length of equilateral triangle

St1: l = (2/3)*a
Area of equilateral triangle = ($$\sqrt{3}$$/4)*a^2 ----- (1)

Area of square = (4/9)*a^2 ----- (2)

(1)/(2) = Area of eqt. triangle/Area of square = (9*$$\sqrt{3}$$)/16 = 9*(1.7)/16 = 15.3/16
Area of equilateral triangle = 0.9 * Area of square
Hence Area of equilateral triangle < Area of square
Sufficient

St2: Perimeter of triangle + Perimeter of square = 17
3a + 4l = 17 --> We have two unknowns.
If a = 1/3 and l = 4 then Area of square > Area of eqt. triangle
If l = 1/2 and a = 5 then Area of eqt. triangle > Area of square
Not Sufficient

Retired Moderator
Joined: 07 Jan 2016
Posts: 1090
Location: India
GMAT 1: 710 Q49 V36
Re: Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

### Show Tags

23 Feb 2018, 02:30
AbdurRakib wrote:
Is the area of equilateral triangle E less than the area of square C ?

(1) A side of square C is $$\frac{2}{3}$$ the length of a side of triangle E.

(2) The sum of the perimeters of triangle E and square C is 17

square's side 2/3of the equilateral triangles side

unique value obtained

ex - side of square = 2 side of triangle = 3

area of square = 4

area of equilateral triangle = rt3 /4 x 3 x 3 on calculation we can know the value

sufficient

(2) perimeter = 17

multiple solutions for perimeter possible

4a +3b = 17

no unique ans

(A) imo
Manager
Joined: 26 Sep 2016
Posts: 58
Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

### Show Tags

23 Feb 2018, 16:26
If we name one side of the square c and one side of the triangle e, the square's area will be $$c^2$$ and equilateral triangle's area will be $$e^2 \sqrt{3}/4$$ We need to know whether the area of equilateral triangle E is less than the area of square C .

(1) A side of square C is 2/3 the length of a side of triangle E.

As we know the relationship between the sides, we can assign any numbers in this ratio as the sides of the square and triangle in our formulas for the areas of square and triangle and it will show us which one is larger. sufficient.

(2) The sum of the perimeters of triangle E and square C is 17

This statement just shows that 3e+4c=17 so e and c can take various values which would change the areas of square and triangle. Not sufficient

Is the area of equilateral triangle E less than the area of square C ?   [#permalink] 23 Feb 2018, 16:26
Display posts from previous: Sort by