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# An equalateral triangle is cut in half. If the height of

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An equalateral triangle is cut in half. If the height of [#permalink]

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18 Oct 2007, 05:40
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An equalateral triangle is cut in half.
If the height of one of the triangles is 4 root(3),
what is the perimeter of the entire triangle?
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Director
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Re: Perimeter of an equilateral triangle - PS [#permalink]

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18 Oct 2007, 06:01
An equalateral triangle is cut in half.
If the height of one of the triangles is 4 root(3),
what is the perimeter of the entire triangle?

cut in half means we have now two 30-60-90 triangles.

for 30:60:90 triangle sides map out like:
s : sqrt(3) * s : 2s

4 : 4 root(3) : 8

8 is the one side of equilateral triangle, so perimeter=8*3=24
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18 Oct 2007, 11:11
i agree with asaf, it is 24. Like he said 30-60-90 angles. we get x, 2x and sq rt 3. Since we know the height is 4sq rt 3, therefore x is 4. 2x, which is the side of the equilateral triangle is 8. Now 8x3 is 24.
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Re: Perimeter of an equilateral triangle - PS [#permalink]

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18 Oct 2007, 18:48
An equalateral triangle is cut in half.
If the height of one of the triangles is 4 root(3),
what is the perimeter of the entire triangle?

Let`s say triangle ABC, where D is a mid point between A and C is cut into two, so that D is right angle.

since there are two heights, there are two possible anwers..

1) DC is 4root(3), then Perimeter is 2*4root(3)+2*2*4root(3)=24root(3), thus perimeter is 24root(3)
2) BD is 4root(3), then since DC=BC/2----------> BC^2=(BC/2)^2+BD^2

plug in value of BD, we get BC^2=(BC/2)^2+48--------> BC^2=64, thus BC=8. if BC is 8, then perimeter is 24

......?
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Re: Perimeter of an equilateral triangle - PS [#permalink]

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18 Oct 2007, 18:52
An equalateral triangle is cut in half.
If the height of one of the triangles is 4 root(3),
what is the perimeter of the entire triangle?

if the question was

An equalateral triangle is cut in half.
If the height of that triangle is 4 root(3),
what is the perimeter of the entire triangle?

the answer would be 24.
Re: Perimeter of an equilateral triangle - PS   [#permalink] 18 Oct 2007, 18:52
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# An equalateral triangle is cut in half. If the height of

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