Equilateral triangle is x square meters

Question

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}

Can someone please explain me the solution for this problem?

einstein10 · Answer

for equilateral triangle, area 
  A = \frac{ \sqrt3}{4}*a^2  ---------(1)

where a is length of one side

and perimeter  P = 3*a  -----(2)

it is given that perimeter(  p=x ) and area(  A=x ) are same

so  A=p

or  \frac{ \sqrt3}{4}*a^2 = 3*a

or  \frac{ \sqrt3}{4}*a = 3

or  a = \frac{3*4}{\sqrt3}

==>  a = 4*\sqrt3

length of one side of the triangle in meters =  4*\sqrt3 
hope this helps thanks

fivezero7 · Answer

hi,
the perimeter of the given equilateral triangle is x meters.
so each side will be x/3 meters.

now area of an equilateral triangle is  A = \frac{\sqrt 3}{4} * a^2  where a is the side.
putting the values here, we get
 x = \frac{\sqrt 3}{4} * (\frac {x}{3})^2 
solving for x we get,
 x = 4*3\sqrt 3 
hence each side will be
 \frac {x}{3} = 4 \sqrt 3

ronny13 · Answer

Area of triangle = (sqrt3/4) s^2 = x meters^2

Perimeter of triangle = 3s = x meters

Equate both of them:
(sqrt3/4) s^2 = 3s
After Solving we get, s= 4(sqrt3)

We need length of one side: s/3 = 4(sqrt3)/3 = 4/sqrt3

Ans: E

---------------------------------
- Prince

zz0vlb · Answer

Thank you all. Its very clear now.

Equilateral triangle is x square meters

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards