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

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) (Show Source): You can put this solution on YOUR website!
Let be the length of one of the pieces, in cm.
= the length of the other piece, in cm.
The sides of the squares made will measure and cm,
and the areas of those squares, in square cm, will be
and respectively.
The total area of ththe two squares, in square cm, will be

That expression, like is a quadratic function of .
Quadratic functions have the general form ,
and if the quadratic function has a minimum at .
Both, and , have a minimum at
--> .
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.
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