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

Redeem

Can anyone help me figure this one out?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Wed Apr 25, 2012 11:35 am

Can anyone help me figure this one out?

by debonairdrz » Wed Apr 25, 2012 12:01 pm
If the area of an equilateral triangle is x square meters and the perimeter is x meters, then
what is the length of one side of the triangle in meters?

(A)6
(B)8
(C)4 sqrt(2)
(D)2 sqrt(3)
(E)4 sqrt(3)


I apologize, this is my first post, and formatting's not my strong suit. Answers C,D,E are "four times the square root of two", "two times the square root of three", and "four times the square root of three", respectively.


I can't figure out what I'm doing wrong with this one. If the perimeter is the same as the area, I can set up an equation as follows:

x = length of one side (I know that in the wording of the problem x is used differently, but I like x. Please humor me.)

3x=(1/2)xh

Since it is an equilateral triangle, the height will be (sqrt(3)/2)X (I think this is necessarily the case since when we draw in the height we create a 30-60-90 triangle and 30-60-90 triangles have side lengths with the ratio of 1 - sqrt(3) - 2.

Therefore I now have:

3x=(1/2)x sqrt(3)(x/2)


That's where I get stuck. Whenever I solve this my answer matches none of the possible answers. Am I messing up the algebra or do I have the problem set up incorrectly?

Any and all help is greatly appreciated.
Top
Source: — Problem Solving |
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Fri Apr 06, 2012 1:27 am
Thanked: 5 times
Followed by:1 members
GMAT Score:770

by Mr Smith » Wed Apr 25, 2012 12:28 pm
hey debonairdrz,

U have got it right till the equation.
U are doing something wrong while simplyfying it.

3x = sqrt(3)*(x^2)/4
Thus x/4 = 3/sqrt(3)
Thus x = 4*sqrt(3)

Note: I am following the same nomenclature as you are n the solution. as in x is the side of the triangle :)
Kindly Use Thanks Button as liberally as you receive replies. :)

Mr. Smith
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Wed Apr 25, 2012 7:42 pm
Mr Smith wrote:hey debonairdrz,

U have got it right till the equation.
U are doing something wrong while simplyfying it.

3x = sqrt(3)*(x^2)/4
Thus x/4 = 3/sqrt(3)
Thus x = 4*sqrt(3)

Note: I am following the same nomenclature as you are n the solution. as in x is the side of the triangle :)
Perfect solution, just to clarify a few steps:

3x = sqrt(3)*(x^2)/4

We know that x is positive (since it's the side of a triangle), so we can safely divide both sides by x to get:

3 = sqrt3 * x/4

Multiplying both sides by 4:

12 = sqrt 3 * x

Dividing both sides by sqrt3:

12/sqrt3 = x

It's mathematically inelegant to leave a root in the denominator of a fraction, so we "rationalize the denominator" by multiplying the fraction by (root we want to get rid of / root we want to get rid of). Accordingly:

12*sqrt3/sqrt3*sqrt3 = x
12(sqrt3)/3 = x
4(sqrt3) = x
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Tue Jan 31, 2012 6:50 am
Location: New Delhi
Thanked: 16 times
Followed by:2 members
GMAT Score:760

by nisagl750 » Thu Apr 26, 2012 12:20 am
debonairdrz wrote:If the area of an equilateral triangle is x square meters and the perimeter is x meters, then
what is the length of one side of the triangle in meters?

(A)6
(B)8
(C)4 sqrt(2)
(D)2 sqrt(3)
(E)4 sqrt(3)


I apologize, this is my first post, and formatting's not my strong suit. Answers C,D,E are "four times the square root of two", "two times the square root of three", and "four times the square root of three", respectively.


I can't figure out what I'm doing wrong with this one. If the perimeter is the same as the area, I can set up an equation as follows:

x = length of one side (I know that in the wording of the problem x is used differently, but I like x. Please humor me.)

3x=(1/2)xh

Since it is an equilateral triangle, the height will be (sqrt(3)/2)X (I think this is necessarily the case since when we draw in the height we create a 30-60-90 triangle and 30-60-90 triangles have side lengths with the ratio of 1 - sqrt(3) - 2.

Therefore I now have:

3x=(1/2)x sqrt(3)(x/2)


That's where I get stuck. Whenever I solve this my answer matches none of the possible answers. Am I messing up the algebra or do I have the problem set up incorrectly?

Any and all help is greatly appreciated.
I guess your equation read like:
3x = (1/2)x*sqrt(3)(x/2)
Simplifying it we get
3x = sqrt(3)/4*x^2

Solving this we get x=12/sqrt(3)

Hope you got this answer.
Now all you hacve to do is rationalise it.

i.e. multiply and divide it by sqrt(3)
So you'll get X=4*sqrt(3)

Hope it helps ;)
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Apr 26, 2012 12:32 am
debonairdrz wrote:If the area of an equilateral triangle is x square meters and the perimeter is x meters, then
what is the length of one side of the triangle in meters?

(A)6
(B)8
(C)4 sqrt(2)
(D)2 sqrt(3)
(E)4 sqrt(3)


I apologize, this is my first post, and formatting's not my strong suit. Answers C,D,E are "four times the square root of two", "two times the square root of three", and "four times the square root of three", respectively.


I can't figure out what I'm doing wrong with this one. If the perimeter is the same as the area, I can set up an equation as follows:

x = length of one side (I know that in the wording of the problem x is used differently, but I like x. Please humor me.)

3x=(1/2)xh

Since it is an equilateral triangle, the height will be (sqrt(3)/2)X (I think this is necessarily the case since when we draw in the height we create a 30-60-90 triangle and 30-60-90 triangles have side lengths with the ratio of 1 - sqrt(3) - 2.

Therefore I now have:

3x=(1/2)x sqrt(3)(x/2)


That's where I get stuck. Whenever I solve this my answer matches none of the possible answers. Am I messing up the algebra or do I have the problem set up incorrectly?

Any and all help is greatly appreciated.
Another approach is to plug in the answers, which represent the length of each side of the triangle.
It is helpful to know the formula for the area of an equilateral triangle:
A = (s²√3)/4.

Since p=3s, we get:

3s = (s²√3)/4.

For the lefthand side to be equal to the righthand side, the value of s almost certainly will include a factor 4 and a factor of √3.

Answer choice E: 4√3
Plugging this value into 3s = (s²√3)/4, we get:
3(4√3) = ((4√3)²*√3)/4
12√3 = ((16*3)√3)/4
12√3 = 12√3.
Success!

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1