precalculus A wire 100 centimeters in length is cut into two

A wire 100 centimeters in length is cut into two pieces. One piece is bent to form a square and the other to form other to form a circle. Let x equal the length of the wire used to form the Square. (a) Write the function that represents the area of the two figures. (b) Determine the domain of the function. (c) Find the value(s) of x that yield a maximum a minimum area. d) Explain your reasoning.

Solution

a. Let the side of the square be y.

perimeter of square

4y=x

y=x/4

circumference of circle , 100- x=2pi r

r=(100-x)/2pi

Area,A(x)= (x/4)² + (100-x)²/4

b. Domain is [0,100)