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If the area of an equilateral triangle is x square meters [#permalink]

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29 Dec 2010, 18:25

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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?

Keep coming up with the wrong answer for this one! Any help would be greatly appreciated.

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√2 D 2√3 E 4√3

Let me try

Area of Equilateral triangle = perimeter \sqrt{3/4}* \(S^2\) = 3S

Simplifying the above equation would give E
_________________

Keep coming up with the wrong answer for this one! Any help would be greatly appreciated.

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√2 D 2√3 E 4√3

If perimeter of equilateral triangle is x, its side must be x/3. If side is x/3, its area must be \((\sqrt{3}/4)*(x/3)^2\)[Area of equilateral triangle of side 'a' is \((\sqrt{3}/4)*a^2\)] Area of triangle = \(x = (\sqrt{3}/4)*(x/3)^2\) \(3*(4/\sqrt{3}) = x/3\) \((4\sqrt{3}) = x/3\) = side of the triangle
_________________

i think we cannot solve it without formula and if we know formula it will hardly take a minute to crack it........ appreciated if some one help us to solve it without formula.

is there any other way solving the problem without using the area-formula for equilateral triangle?

If you don't know the equilateral triangle area formula, you will need to use the area formula for any triangle i.e. (1/2)*base*altitude You will get the area for the equilateral triangle.

Since perimeter = x meters, length of side = x/3 meters.

So base = x/3 What about the altitude? You need to use pythagorean theorem to figure it out. The altitude bisects the opposite side in an equilateral triangle so (x/3)^2 = (x/6)^2 + altitude^2 altitude =\(x/(2\sqrt{3})\)

Area of triangle = \((1/2)*(x/3)*(x/(2\sqrt{3}) = x^2/12*\sqrt{3}\)

This is the same as the formula (obviously!)\(\sqrt{3}/4 * (x/3)^2 = x^2/12*\sqrt{3}\)
_________________

HI, can anyone explain how to get to the correct answer from here: (S^2*Square3)/4=3S.... I got S=12/square3 thanks!!

Length of the side = S/3 not S. S is the perimeter of the triangle (actually it is given as x in the original question) So area =\(((S/3)^2*\sqrt{3})/4 = S\) You get \(S = 12*\sqrt{3}\) Length of side = \(S/3 = 12*\sqrt{3}/3 = 4*\sqrt{3}\)
_________________

Re: If the area of an equilateral triangle is x square meters [#permalink]

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29 Jul 2013, 03:18

m990540 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√2 D 2√3 E 4√3

Understanding the question: Questions talks about area, perimeter and side of an equilateral triangle.

Facts to refer: Area of an equilateral triangle = (sqrt(3)/4)*a^2. As suggested by Karishma, if this formula is not known, then one can use the normal formula for area of triangle, (1/2 * bh), consider the 30-60-90 ratio and find the height. But knowing this formula can save valuable seconds. Perimeter of an equilateral triangle = 3a

What's given in the question and what it implies (noted as =>): Area of an equilateral triangle = Perimeter => (sqrt(3)/4)*a^2 = 3a

What is asked for: Value of a

Solution: Solving (sqrt(3)/4)*a^2 = 3a => a = 4*sqrt(3)

Keep coming up with the wrong answer for this one! Any help would be greatly appreciated.

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√2 D 2√3 E 4√3

If perimeter of equilateral triangle is x, its side must be x/3. If side is x/3, its area must be \((\sqrt{3}/4)*(x/3)^2\)[Area of equilateral triangle of side 'a' is \((\sqrt{3}/4)*a^2\)] Area of triangle = \(x = (\sqrt{3}/4)*(x/3)^2\) \(3*(4/\sqrt{3}) = x/3\) \((4\sqrt{3}) = x/3\) = side of the triangle

Dear Karishma, I lost you way on step: (S/3)^2 * sqrt3/4=S After this step my simplifications I always get: S/3=12/sqrt3

here my calculation: (S/3)^2 * sqrt3/4=S---> S^2/9 * sqrt3/4=S---> S^2*sqrt3 / 36=S---> S^2*sqrt3 / S =36---> S* sqrt3=36---> S= 36/ sqrt3---> here we need to divide by 3 in order to find S/3---> s/3= 12/sqrt3

I understant that is just small silly mistake somewhere but I could not spot it Please help me out Many thanks
_________________

Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen...

Keep coming up with the wrong answer for this one! Any help would be greatly appreciated.

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√2 D 2√3 E 4√3

If perimeter of equilateral triangle is x, its side must be x/3. If side is x/3, its area must be \((\sqrt{3}/4)*(x/3)^2\)[Area of equilateral triangle of side 'a' is \((\sqrt{3}/4)*a^2\)] Area of triangle = \(x = (\sqrt{3}/4)*(x/3)^2\) \(3*(4/\sqrt{3}) = x/3\) \((4\sqrt{3}) = x/3\) = side of the triangle

Dear Karishma, I lost you way on step: (S/3)^2 * sqrt3/4=S After this step my simplifications I always get: S/3=12/sqrt3

here my calculation: (S/3)^2 * sqrt3/4=S---> S^2/9 * sqrt3/4=S---> S^2*sqrt3 / 36=S---> S^2*sqrt3 / S =36---> S* sqrt3=36---> S= 36/ sqrt3---> here we need to divide by 3 in order to find S/3---> s/3= 12/sqrt3

I understant that is just small silly mistake somewhere but I could not spot it Please help me out Many thanks

Here is how I did it:

We know that the side (S) = x and the area (A) = x^2

The area of an equilateral triangle = √(3) / 4 * s^2

Keep coming up with the wrong answer for this one! Any help would be greatly appreciated.

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√2 D 2√3 E 4√3

If perimeter of equilateral triangle is x, its side must be x/3. If side is x/3, its area must be \((\sqrt{3}/4)*(x/3)^2\)[Area of equilateral triangle of side 'a' is \((\sqrt{3}/4)*a^2\)] Area of triangle = \(x = (\sqrt{3}/4)*(x/3)^2\) \(3*(4/\sqrt{3}) = x/3\) \((4\sqrt{3}) = x/3\) = side of the triangle

Dear Karishma, I lost you way on step: (S/3)^2 * sqrt3/4=S After this step my simplifications I always get: S/3=12/sqrt3

here my calculation: (S/3)^2 * sqrt3/4=S---> S^2/9 * sqrt3/4=S---> S^2*sqrt3 / 36=S---> S^2*sqrt3 / S =36---> S* sqrt3=36---> S= 36/ sqrt3---> here we need to divide by 3 in order to find S/3---> s/3= 12/sqrt3

I understant that is just small silly mistake somewhere but I could not spot it Please help me out Many thanks

Your solution is correct. NOte that I get : \(x/3 = (4\sqrt{3})\) = side of the triangle You get \(S/3=12/\sqrt{3}\)

They are the same. You just need to further simplify to rationalize the denominator.

Re: If the area of an equilateral triangle is x square meters [#permalink]

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25 Jul 2014, 03:42

VeritasPrepKarishma wrote:

Saurajm wrote:

HI, can anyone explain how to get to the correct answer from here: (S^2*Square3)/4=3S.... I got S=12/square3 thanks!!

Length of the side = S/3 not S. S is the perimeter of the triangle (actually it is given as x in the original question) So area =\(((S/3)^2*\sqrt{3})/4 = S\) You get \(S = 12*\sqrt{3}\) Length of side = \(S/3 = 12*\sqrt{3}/3 = 4*\sqrt{3}\)

Hey Guys,

sorry to bring this topic up again. I got the right answer by being 80 % sure-guessing, but I couldn't calculate as you did.

Let's say side of triangle = a.

Then: perimeter = x = 3a area = x = \(a^2*\sqrt{3}/4\)

Your math is fine, but you haven't answered the question that was ASKED.

In your last 'step', you've figured out the value of X. The question asks for the length of ONE SIDE of the triangle; X is the PERIMETER of the equilateral triangle, so you have to divide this result by 3 to get the correct answer.

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