SOLUTION: A piece of 2m long wire is to be cut into two pieces one of which is to be formed into a circle and the other into an equilateral triangle. How should the wire be cut so that the t
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Question 980808: A piece of 2m long wire is to be cut into two pieces one of which is to be formed into a circle and the other into an equilateral triangle. How should the wire be cut so that the total area enclosed is (a) a minimum and (b) a maximum
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Cut into pieces x and y.
.
The circle:
, because the length x now is used as the circumference.
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area of this circle,
The equilateral triangle:
Perimeter is y.
This triangle composed of side , and there are two associated 30-60-90 triangles making the equilateral triangle, with short leg . Other leg will be the "height" of the equilateral triangle:
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h, the altitude.
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Area of this equilateral triangle, ,
Total Area,
Next is decide, do you want to substitute for x, or substitute for y?
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MIN or MAX FOR FUNCTION, A:
Find derivative dA/dx, set equal to 0, solve for x. This should be straightforward if you already know how to do this from Calculus 1
(Placing graph of A(x) here):
Expect a minimum at x slightly less than 1.
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