My Math Forum Problem for middle school students

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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 $a=b=c=x;$ 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.)
 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... $\sqrt[11]{7}$ $\sqrt[\pi]{\gamma}$ 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 $s$ be the side length, we may state: $A=\frac{s^2}{2}\sin$$60^{\circ}$$=1$ $s^2\cdot\frac{\sqrt{3}}{2}=2$ $s^2=\frac{4}{\sqrt{3}}$ 
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 $s$ be the side length, the we may state: $A=\frac{s^2}{2}\sin$$60^{\circ}$$=1$ $s^2\cdot\frac{\sqrt{3}}{2}=2$ $s^2=\frac{4}{\sqrt{3}}$ 
Very nicely done!

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
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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

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

$A \= \ \frac{1}{2}b \cdot h \$ and $\ a^2 \ + \ b^2 \= \ c^2$

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

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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