How do I do this problem? Express the area A of an equilateral triangle as a function of the perimeter P.
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here's a place to start ... what is the area of an equilateral triangle in terms of one of its sides, "s" ?
It's (sē√3)/(4), I looked it up, but how does one get there?
Last edited by RaphaelB30; Nov 30th 2008 at 02:08 PM. Reason: Typed wrong number
well, what's the relationship between a side, "s", and the perimeter, "P" ?
P=3S, Since an equilateral triangle has equal S's, would I just put a 3 next to the S, making the final answer, (3sē√3)/(8)
no ... $\displaystyle s = \frac{P}{3}$ substitute that in for "s" in your original area equation
ok...would that mean the answer is ((pē/9)√3)/(4)?
Last edited by RaphaelB30; Nov 30th 2008 at 02:30 PM. Reason: Typed wrong number
I think I got it, thanks...the answer is... ((pē√3)/(36)
clean it up ... $\displaystyle A = \frac{P^2 \sqrt{3}}{36}$
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