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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
Equilateral triangle is x square meters [#permalink]

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20 Apr 2010, 21:09
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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?

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Manager
Joined: 13 Dec 2009
Posts: 127

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Re: Equilateral triangle is x square meters [#permalink]

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20 Apr 2010, 21:23
1
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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

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Intern
Joined: 08 Apr 2010
Posts: 28

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Re: Equilateral triangle is x square meters [#permalink]

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20 Apr 2010, 22:44
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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Intern
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Re: Equilateral triangle is x square meters [#permalink]

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21 Apr 2010, 01:13
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

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Manager
Joined: 27 Feb 2010
Posts: 106

Kudos [?]: 440 [0], given: 14

Location: Denver
Re: Equilateral triangle is x square meters [#permalink]

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21 Apr 2010, 18:07
Thank you all. Its very clear now.

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Re: Equilateral triangle is x square meters   [#permalink] 21 Apr 2010, 18:07
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