Posted by **Matt** on Thursday, December 2, 2010 at 10:51pm.

A wire 100 inches long is to be cut into two pieces. One of the pieces will be bent into the shape of a circle and the other into the shape of a equilateral triangle. How should the wire be cut so as to maximize the sum of the area of the areas of the circle and triangle will be maximized?

- Calc -
**MathMate**, Thursday, December 2, 2010 at 11:01pm
L=total length,

x=length of piece for triangle

So

L-x=circumference of circle

At(x)=area of triangle

=√3 *x²/4

Ac(x)=area of circle

=π((L-x)/(2π))²

=(L-x)²/(4π)

Total Area, A(x)

= At(x)+Ac(x)

To find the maximum/minimum,

Equate

A'(x)=0 and solve for x.

Find A(x) = max. area.

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