A rectangular field is twice as long as it is wide. Express the area of the rectangle as a function of the perimeter, P.
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A rectangular field is twice as long as it is wide. Express the area of the rectangle as a function of the perimeter, P.
Perimeter = 2*Length + 2*Width
2W = L
Perimeter = 6*Width
Area = Length*Width = Width*2*Width = 2W2
(6*Width)2/18 = 2W2 so (Perimeter2)/18 = Area (here I squared and then divided both sides of the Perimeter = ... equation by 18 and substituted)
I think I'm right, not 100% sure though.
ok, lets say you have a perimeter of P.
P/6 is then the number of arbitury unit lengths (it's 12:33 am here so I'm tired). Now call that L.
2L*L should be A
so 2(P/6) * (P/6)
0.5A = (P/6)^2
6sqrt[.5A] = P
I think thats right
acidic: i haven't done that problem myself yet, but i think that's right
width =2x, height = x
area = width*height
area = 2x*x = 2x^2
perimeter = width + height
perimeter = 2x+x = 3x
soooo
assuming
P(3x) = 2x^2
P(x) = 2(x/3)^2
p(x) = 2x^2/9
p(x) = x^2 / 4.5
OK, I think I was right earlier but here is some working out easier to follow:
A = 1/6P * 1/3P
A = 1/18P^2
18A = P^2
sqrt[18A] = P
or:
3*sqrt[6A] = P
which ever you prefer. :)
Well...
w=p/3
h=p/6
Thus... a=p^2/18
so...
p=3*sqr(2a)
sqrt(18a) = 3*sqrt(2a)Quote:
Originally posted by Acidic
OK, I think I was right earlier but here is some working out easier to follow:
A = 1/6P * 1/3P
A = 1/18P^2
18A = P^2
sqrt[18A] = P
or:
3*sqrt[6A] = P
which ever you prefer. :)
3*3 = 9 * 2 = 18
:p
wouldn't that be sqrt(54A) instead of sqrt(18A)?Quote:
Originally posted by Acidic
sqrt[18A] = P
or:
3*sqrt[6A] = P
which ever you prefer. :)
...because 3 * sqrt(6A) = sqrt(9) * sqrt(6A) = sqrt(54A)
He took the 3 out correctly, but forget it's sqrt(9)*sqrt(2)=sqrt(18), not... what he did.Quote:
Originally posted by dolor
wouldn't that be sqrt(54A) instead of sqrt(18A)?
...because 3 * sqrt(6A) = sqrt(9) * sqrt(6A) = sqrt(54A)
ahh, i see now. thxQuote:
Originally posted by DiGiTaIErRoR
He took the 3 out correctly, but forget it's sqrt(9)*sqrt(2)=sqrt(18), not... what he did.
Yes, my error, sorry.
dont be..its no biggieQuote:
Originally posted by Acidic
Yes, my error, sorry.