1. Divide wire b in parts x and b-x.
2. Bend the b-x piece to form a triangle with side (b-x)/3
There are many ways to find the area of the equilateral triangle. One is by the formula A=
A=
Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6
3. Let x be the circumference of the circle.
so
Area of circle =
4. Let f(x)=
be the function of the sum of the areas of the triangle and circle.
5. f(x) is a minimum means f'(x)=0
f'(x)=
=0
6. So one part is
and the other part is b-
2. Bend the b-x piece to form a triangle with side (b-x)/3
There are many ways to find the area of the equilateral triangle. One is by the formula A=
A=
Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6
3. Let x be the circumference of the circle.
so
Area of circle =
4. Let f(x)=
be the function of the sum of the areas of the triangle and circle.
5. f(x) is a minimum means f'(x)=0
f'(x)=
6. So one part is