A rope 8 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.
1st piece: x feet 2nd piece: 8-x feet -------------------------- Use the "x" piece to form a circle: Circumference = "x". 2(pi)*radius = x
radius = x/(2pi) So, Area = pi[x/(2)]^2 = x^2/(4pi) = (1/4pi)x^2 ========================================================= Use the 10-x piece to form square: side = (1/4pi)(10-x) Area = side^2 = (1/16)(10-x)^2
