Question

A piece of wire 40 m long is cut into two pieces. One piece is bent
into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a
maximum=
minimum=
Find the length of the wire used

Answer 1

If the sides are s and , respectively,

4s+3t = 40
a = √3/4t^2 + s^2

now express a as a function of s (or t) only, and find its extrema (where a'=0)

Answer 2

(sqrt(3)/4)t^2+((40-3t)/4)^2

Answer 3

81