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# Equilateral triangle is x square meters

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Manager
Joined: 27 Feb 2010
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Location: Denver
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Equilateral triangle is x square meters [#permalink]  20 Apr 2010, 20:09
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Question Stats:

75% (01:56) correct 25% (00:43) wrong based on 33 sessions
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?
Manager
Joined: 13 Dec 2009
Posts: 130
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Re: Equilateral triangle is x square meters [#permalink]  20 Apr 2010, 20:23
1
KUDOS
zz0vlb 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}

Can someone please explain me the solution for this problem?

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
Intern
Joined: 08 Apr 2010
Posts: 29
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Re: Equilateral triangle is x square meters [#permalink]  20 Apr 2010, 21:44
zz0vlb 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}

Can someone please explain me the solution for this problem?

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
$$\frac {x}{3} = 4 \sqrt 3$$
_________________

CHEERS
fivezero7

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Re: Equilateral triangle is x square meters [#permalink]  21 Apr 2010, 00:13
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
Manager
Joined: 27 Feb 2010
Posts: 106
Location: Denver
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Kudos [?]: 156 [0], given: 14

Re: Equilateral triangle is x square meters [#permalink]  21 Apr 2010, 17:07
Thank you all. Its very clear now.
Re: Equilateral triangle is x square meters   [#permalink] 21 Apr 2010, 17:07
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