Question 101
Augusto has a wire with $10~\mathrm{m}$ long. He performs a cut at a point on the wire, thus obtaining two wires. One with length $x$ and the other with length $10-x$ as shown in the figure below: 
Augustus uses the two pieces of the wire to make two squares.
a) What is the length of the side of each of the squares? What is the area of each?
b) What is the length value of each of the two pieces of the wire so that the sum of the areas of the squares obtained is minimal?
c) Suppose Augusto cut the wire into ten pieces and use each of them to make a square. What should be the size of each of the pieces so that the sum of the areas of the squares obtained is minimal?
Augustus uses the two pieces of the wire to make two squares. a) What is the length of the side of each of the squares? What is the area of each?
b) What is the length value of each of the two pieces of the wire so that the sum of the areas of the squares obtained is minimal?
c) Suppose Augusto cut the wire into ten pieces and use each of them to make a square. What should be the size of each of the pieces so that the sum of the areas of the squares obtained is minimal?