GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Oct 2019, 18:56

### 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

# If the side of an equilateral triangle decreased by 20%, its area is

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58335
If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

### Show Tags

30 Jan 2019, 01:56
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:23) correct 26% (02:02) wrong based on 45 sessions

### HideShow timer Statistics

If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

_________________
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1028
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

### Show Tags

30 Jan 2019, 02:32
1
Let the side of an equilateral triangle be a.
Area is $$\sqrt{3}/4*a^2$$.
Now, the side becomes 0.8a,
New Area = $$\sqrt{3}/4(0.8a)^2$$ = $$\sqrt{3}/4*0.64a^2$$

% change = $$\frac{New-Old}{Old}$$*100 = 0.36*100 = 36%

_________________
Press +1 Kudos If my post helps!
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4976
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

### Show Tags

30 Jan 2019, 02:55
Bunuel wrote:
If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

let side be 10 and later 20% less 80
area with side 10 = 25 sqrt 3 and with side 8- 16 sqrt 3
so % decrease = 9 /25
36 %
IMO A
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Director
Joined: 09 Mar 2018
Posts: 997
Location: India
Re: If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

### Show Tags

30 Jan 2019, 03:05
Bunuel wrote:
If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

Let the side be 100, Initial Area = 2500 root3

After reduction each side became 80
New area = 1600 root3

Difference between areas = 900 root3

900/2500 *100

Area was decreased by 36%

IMO A

Posted from my mobile device
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

### Show Tags

01 Feb 2019, 18:47
Bunuel wrote:
If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

We use the formula for the area of an equilateral triangle: (a^2 x √3)/4, where a is the side. If the initial side is 10, then the original area is (10^2 x √3)/4 = 100√3/4 = 25√3.

Since the side decreased by 20%, the new side is 8, and the new area is (8^2 x √3)/4 = 64√3/4 = 16√3.

We use the percent change formula: (New - Old)/Old x 100. The percent change is:

(16√3 - 25√3)/25√3 x 100

-9√3/25√3 x 100

-9/25 x 100 = -36%, which is a 36% decrease.

Alternate solution:

We can use the fact that if a side of a regular polygon (equilateral triangle, square, regular pentagon, etc.) is increased or decreased such that the side’s new length is n times its original length, then the new area of the polygon is n^2 times its original area.

Since here the side of an equilateral triangle decreased by 20%, the side’s new length is 0.8 times its old length and thus the new area of the equilateral triangle is 0.8^2 = 0.64 times its original area, i.e., 64% of its original area. We see that this is a 36% decrease.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: If the side of an equilateral triangle decreased by 20%, its area is   [#permalink] 01 Feb 2019, 18:47
Display posts from previous: Sort by