Question

A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Round your answers to two decimal places.)

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

Answer 1

To maximize the total area, we should use 7 meters of wire for the square.

Step-by-step explanation:

To maximize the total area, we need to find the lengths of the wire that will result in the greatest area for both the square and equilateral triangle. Let's start with the square:

The wire for the square consists of 4 sides of equal length. Let's call the length of each side 'x'.

Since the total length of the wire is 28 m, the equation for the perimeter of the square is 4x = 28. Solving for x, we find that x = 7.

Therefore, to maximize the total area, we should use 7 meters of wire for the square.