A rope 16 feet long is cut into two pieces. one piece is used to form a circle and the other used to form a square. find a function representing the area of both square and circle as a function of the length of one side of the square.

Circumference of Circle=C, = 2 (pi) (radius)

Radius of Circle=r

Side of square=x

f (x) = area of circle

g (r) = area of square

16 feet=C+4x

C=16-4x

2 (pi) (r) = 16-4x

2 (pi) (r) = 2 (8-2x)

(pi) (r) = 8-2x

r = (8-2x) / (pi)

x = (8 - (pi) r) / 2

f (x) = (pi) (r^2)

f (x) = (pi) ((8-2x) / (pi)) ^2

f (x) = ((8-2x) ^2) / (pi)

f (x) = ((64-32x+4x^2)) / (pi)

g (r) = ((8 - (pi) r) / 2) ^2

g (r) = ((64-16 (pi) r + (pi) ^2 (r^2)) / 4