A piece of wire 30 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.)

Question

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

s represents the side of the square

30 - 4s represents the perimeter of the triangle.

(30 - 4s) / 3 represents a side of the triangle.

A_triangle = (10 - (4/3)s)² √3 / 3

A_square = s²

The the two, differentiate and answer.