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June 10th, 2013, 10:41 PM   #1
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Problem for middle school students

Find the side length of an equilateral triangle with area 1 square unit.

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June 12th, 2013, 06:45 PM   #2
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Re: Problem for middle school students

If in Heron’s formula
Then s=3/2x
Then the area T=1=?(3/2 x?(3/2 x-x)?^3 )=?(1/2 x)?^2 ?3;
x= 2/?3=2/3 ?(3.)
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June 12th, 2013, 07:12 PM   #3
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2/?3 ? 2/3 ?(3)
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June 12th, 2013, 11:27 PM   #4
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Re: Problem for middle school students

State the exact value please, then rationalize the denominator. You can use the code \sqrt[n]{m} between latex tags, for example...





etc.

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June 13th, 2013, 06:28 AM   #5
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Re: Problem for middle school students

If we let be the side length, we may state:







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June 13th, 2013, 07:13 AM   #6
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Re: Problem for middle school students

Quote:
Originally Posted by MarkFL
If we let be the side length, the we may state:







Very nicely done!

Look at that fourth root of 3 creeping in there.
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June 13th, 2013, 08:01 AM   #7
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Not everyone in middle school will have been taught the trigonometric formula for the area of a triangle.
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June 13th, 2013, 08:15 AM   #8
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Re: Problem for middle school students

Quote:
Originally Posted by McPogor
x= 2/?3=2/3 ?(3.)
x= 2/?3=2/3 ?(3)^3

Sorry
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June 13th, 2013, 08:17 AM   #9
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Re:

Quote:
Originally Posted by skipjack
Not everyone in middle school will have been taught the trigonometric formula for the area of a triangle.
That's true but everyone should have seen

and

You can get the result by using these two formulas and a bit of inspiration and perspiration.

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June 13th, 2013, 08:19 AM   #10
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Re: Problem for middle school students

Quote:
Originally Posted by McPogor
Quote:
Originally Posted by McPogor
x= 2/?3=2/3 ?(3.)
x= 2/?3=2/3 ?(3)^3

Sorry
I don't understand this notation, please explain.

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