Im looking for a formmul;ar i could use in a computer program to find the max area of an isosceles triangle where the sides adsd up to a given length.
Hope im describing this right all help would be great thanks you
-Ace
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Im looking for a formmul;ar i could use in a computer program to find the max area of an isosceles triangle where the sides adsd up to a given length.
Hope im describing this right all help would be great thanks you
-Ace
Let b each of the 2 equal sides and c the other one. Then, the perimeter is:
P = c + 2b
and the area:
A = ch/2 where h is the height:
h = Sqr[b2 - (c/2)2]
so that,
A = (c / 2)*Sqr[b2 - (c/2)2]
From the first equation above,
b = (P - c) / 2
and substituting this into the previous equation,
A = (c / 2)*Sqr{[(P - c) / 2]2 - (c/2)2} = (c / 4) Sqr(P2 - 2PC)
Now, to find the maximum area as a function of c, the derivative must be zero. Using R = Sqr(P2 - 2PC):
0 = dA / dc = -(c / 4)*P / R + R / 4 = (P2 - 2Pc) / 4R
so that
0 = P2 - 2Pc
from which,
P = 3c
c = P / 3 and, of course, b = P / 3
and therefore it's a equilateral triangle as we already knew from intuition.
Nice solution and a phrase of wisdom in perfect portuguese "Aquele que não pode perdoar destroi a ponte sobre a qual ele mesmo deve passar".
Rui
Thanks, I found the phrase in a Brazilian web and I liked it very much. I thought it was fair to keep it in the original, although I might have set it to Catalan: "Aquell que no pot perdonar destrueix el pont sobre el qual ell mateix ha de passar".Quote:
Originally Posted by Rassis