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30-60-90 Triangle Property Question

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30-60-90 Triangle Property Question [#permalink] New post 14 Apr 2013, 10:57
The height of an equilateral triangle splits the triangle into two 30-60-90 triangles (Each 30-60-90 triangle has sides in the ratio of 1: square root of 3: 2). Because of this, the area for an equilateral triangle can be expressed in terms of one side. If we call the side of the equilateral triangle, s, the height must be (s multiplied by square root of 3) / 2 (using the 30-60-90 relationships).


Can someone explain why the height which is the square root of 3 is being divided by 2? The explanation then states... "The area of a triangle = 1/2 × base × height, so the area of an equilateral triangle can be expressed as: 1/2 × s × (s multiplied by square root of 3) / 2 .

The question i pulled this from is asking about the area of the triangle. MGMAT's explanation does not make sense to me of why the height is being divided by 2 initially.

Thanks!!!!!!
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Re: 30-60-90 Triangle Property Question [#permalink] New post 14 Apr 2013, 11:23
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Richard0715 wrote:
The height of an equilateral triangle splits the triangle into two 30-60-90 triangles (Each 30-60-90 triangle has sides in the ratio of 1: square root of 3: 2). Because of this, the area for an equilateral triangle can be expressed in terms of one side. If we call the side of the equilateral triangle, s, the height must be (s multiplied by square root of 3) / 2 (using the 30-60-90 relationships).


Can someone explain why the height which is the square root of 3 is being divided by 2? The explanation then states... "The area of a triangle = 1/2 × base × height, so the area of an equilateral triangle can be expressed as: 1/2 × s × (s multiplied by square root of 3) / 2 .

The question i pulled this from is asking about the area of the triangle. MGMAT's explanation does not make sense to me of why the height is being divided by 2 initially.

Thanks!!!!!!


Lets say that the side is s. so the side of the base of the 30-60-90 triangle is s/2. Do you agree? Now the side of the 30-60-90 triangle are in the proportion
1x : x\sqrt{3} : 2x. because 1x is refered to the base and the base = s/2 we can conclude that x=s/2
So the height will be x\sqrt{3} where x=s/2 so H=\frac{s}{2}\sqrt{3}

Let me know if it's clear now
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Re: 30-60-90 Triangle Property Question [#permalink] New post 17 Apr 2013, 10:54
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Richard0715 wrote:
The height of an equilateral triangle splits the triangle into two 30-60-90 triangles (Each 30-60-90 triangle has sides in the ratio of 1: square root of 3: 2). Because of this, the area for an equilateral triangle can be expressed in terms of one side. If we call the side of the equilateral triangle, s, the height must be (s multiplied by square root of 3) / 2 (using the 30-60-90 relationships).


Can someone explain why the height which is the square root of 3 is being divided by 2? The explanation then states... "The area of a triangle = 1/2 × base × height, so the area of an equilateral triangle can be expressed as: 1/2 × s × (s multiplied by square root of 3) / 2 .

The question i pulled this from is asking about the area of the triangle. MGMAT's explanation does not make sense to me of why the height is being divided by 2 initially.

Thanks!!!!!!

Dear Richard,
It appears that Zarrolou already gave a fine explanation to this specific question. Here are a couple links that provide some more background:
http://magoosh.com/gmat/2012/gmat-math- ... emorizing/
http://magoosh.com/gmat/2012/the-gmats- ... triangles/
Let me know if you have any further questions.
Mike :-)
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Mike McGarry
Magoosh Test Prep

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Re: 30-60-90 Triangle Property Question   [#permalink] 17 Apr 2013, 10:54
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