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June 10th, 2013, 10:41 PM  #1 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Problem for middle school students
Find the side length of an equilateral triangle with area 1 square unit. 
June 12th, 2013, 06:45 PM  #2 
Senior Member Joined: Sep 2010 Posts: 221 Thanks: 20  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 xx)?^3 )=?(1/2 x)?^2 ?3; x= 2/?3=2/3 ?(3.) 
June 12th, 2013, 07:12 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,937 Thanks: 2210 
2/?3 ? 2/3 ?(3)

June 12th, 2013, 11:27 PM  #4 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  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. 
June 13th, 2013, 06:28 AM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Problem for middle school students
If we let be the side length, we may state: 
June 13th, 2013, 07:13 AM  #6  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Problem for middle school students Quote:
Look at that fourth root of 3 creeping in there.  
June 13th, 2013, 08:01 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,937 Thanks: 2210 
Not everyone in middle school will have been taught the trigonometric formula for the area of a triangle.

June 13th, 2013, 08:15 AM  #8  
Senior Member Joined: Sep 2010 Posts: 221 Thanks: 20  Re: Problem for middle school students Quote:
Sorry  
June 13th, 2013, 08:17 AM  #9  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Quote:
and You can get the result by using these two formulas and a bit of inspiration and perspiration.  
June 13th, 2013, 08:19 AM  #10  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Problem for middle school students Quote:
 

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