Question

A piece of wire 7 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.

(a) How much wire should be used for the square in order to maximize the total area?
(b) How much wire should be used for the square in order to minimize the total area?

Answer 1

To maximize the total area, the square should be made using 4m of wire. To minimize the total area, the square should be made using 7m of wire.

Step-by-step explanation:

To solve this problem, we need to understand that the perimeter of the square and the perimeter of the equilateral triangle will add up to be the length of the wire, which is 7m.

(a) To maximize the total area, we need to maximize the area of the square. The perimeter of the square is 4 times the length of one side, so let's call the length of one side x. It means that 4x + 3x = 7, since the perimeter of the square and the triangle need to add up to 7. Solving this equation, we find that x = 1.

Therefore, the square should be made using 4m of wire in order to maximize the total area.

(b) To minimize the total area, we need to minimize the area of the square. Again, let's call the length of one side x. It means that 4x + 3x = 7. Solving this equation, we find that x = 7/7 = 1.

Therefore, the square should be made using 7m of wire in order to minimize the total area.

Answer 2

B. How much wire should be used for the square in order to minimize the total area?

Hope I helped! ( Smiles )