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December 7, 2016
Posted by **Ce** on Saturday, September 4, 2010 at 12:23pm.

- Precalculus -
**bobpursley**, Saturday, September 4, 2010 at 1:23pmarea= PI*(L/2)^2 + area of triangle.

Well, it turns out there is a neat formula

area= sqrt(s(s-a)(s-b)(s-c)) where s is the semi perimeter, and a,b,c are sides.

s= 1/2 (3T) where T is triangle side

so areatriangle= sqrt(3T/2)(3T/2-T)^3

= sqrt(3T/2 * T^3/8)=sqrt(3T^4/16)

= T^2/4 * sqrt3

so finally, area total=

PI (L/2)^2+ T^2/4 sqrt3

where 3T+PiL= 200cm

or Area=1/4PI* (200-3T)^2+T^2/4 sqrt4

check that.

Now with calculus, you take the derivative of area, set to zero, and solve for T, then L.

I assume you have not had this, then plot the parabola, find its maximum, and the corresponding T.

Knowing T, cut three pieces T length, and the remainder Pi*L is the circle perimeter.

check my work.