Question

A rope 10 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.

Answer 1

10-x=C=2πr

(10-x)/(2π)=r

A=π(100-20x+x^2)/(4π^2)

A=(x^2-20x+100)/(4π)

...

x/4=s, x=4s using this in the area of a circle we get:

A=(16s^2-80s+100)/(4π)

A=(4s^2-20s+25)/π

And of course the area of a square is s^2

A=(4s^2+πs^2-20s+25)/π