SOLUTION: Bob wants to cut a wire that is 60 cm long into two pieces. Then he wants to make each piece into a square. Determine how the wire should be cut so that the total area of the two s

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Bob wants to cut a wire that is 60 cm long into two pieces. Then he wants to make each piece into a square. Determine how the wire should be cut so that the total area of the two s      Log On


   

Question 928247: Bob wants to cut a wire that is 60 cm long into two pieces. Then he wants to make each piece into a square. Determine how the wire should be cut so that the total area of the two squares is as small as possible.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the length of one of the pieces, in cm.
60-x= the length of the other piece, in cm.
The sides of the squares made will measure x%2F4 and %2860-x%29%2F4 cm,
and the areas of those squares, in square cm, will be
%28x%2F4%29%5E2=x%5E2%2F16 and %28%2860-x%29%2F4%29%5E2=%283600-120x%2Bx%5E2%29%2F16 respectively.
The total area of ththe two squares, in square cm, will be

That expression, like x%5E2-60x%2B1800 is a quadratic function of x .
Quadratic functions have the general form f%28x%29=ax%5E2%2Bbx%2Bc ,
and if a%3E0 the quadratic function has a minimum at x=-b%2F2a .
Both, %28x%5E2-60x%2B1800%29%2F8 and x%5E2-60x%2B1800 , have a minimum at
x=-%28-60%29%2F2-->x=30 .
So, to make the total area of the two squares is as small as possible, the wire should be cut in half, making two 30-cm pieces.