Question

A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Give your answers correct to two decimal places.)(a) How much wire should be used for the square in order to maximize the total area?m(b) How much wire should be used for the square in order to minimize the total area?m

Answer 1

To maximize the total area, set up equations using the length of wire used for the square and the equilateral triangle. To minimize the total area, solve the equations for the minimum length of wire used for the square.

Step-by-step explanation:

In order to maximize the total area, we need to find the length of wire that should be used for the square. Let x represent the length of wire used for the square. The remaining wire will be used for the equilateral triangle, so the length of wire used for the triangle will be 23 - x.

The perimeter of the square is equal to 4 times the length of each side, and the perimeter of the equilateral triangle is equal to 3 times the length of each side. Therefore, we can set up the following equations:

x = 4s

23 - x = 3s

where s is the length of each side.

Solving these equations simultaneously, we can find the length of the wire used for the square.

To minimize the total area, we need to minimize the length of wire used for the square. So we can use the same equations and solve for x again to find the length of wire used for the square.