SOLUTION: Please help me answer this question. A wire 36 m long is cut into two pieces. Each piece is bent to form a rectangle which is 1.0 m longer than it is wide. How long should each

Question 66492: Please help me answer this question.
A wire 36 m long is cut into two pieces. Each piece is bent to form a rectangle which is 1.0 m longer than it is wide. How long should each piece to be minimize the sum of the areas of the two rectangle?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A wire 36 m long is cut into two pieces. Each piece is bent to form a rectangle which is 1.0 m longer than it is wide. How long should each piece to be minimize the sum of the areas of the two rectangle?
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Let the two pieces be x and 36-x
Using the "x" piece to form a proper rectangle get sides of (x-1)/2 and (x+1)/2
This rectangle has Area=(x^2-1)/4
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Using the "36-x" piece to for a proper rectangle get sides of
(35-x)/2 and (37-x)/2
This rectangle has Area=(x^2-72x+(35)(37))/4
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Adding the two area you get (1/4)(2x^2-72x+C), C is a constant
Taking the derivative you get Area'=(1/4)(4x-72)=x-18
Checking for minumum you get x-18=0 or x=18 meters
Each piece should be 18 meters.
Cheers,
Stan H.
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