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.
+808 length of rope: 16 ft
length of one side of the square: x
area of square: As(x) = x2
length of the "square piece": 4x
length of "circle piece": 16 - 4x
We know that: C = 2 * pi * r => r = C/(2 * pi)
Area of cicle: Ac = pi * r2 = pi * [C/(2 * pi)]2 = pi * (C2/4 * pi2)
Ac = C2/4pi = (16 - 4x)2/4pi = 4(4 - x)2/4pi
Ac = (4 - x)2/pi
Ac(x) = (4 - x)2/pi
+808 length of rope: 16 ft
length of one side of the square: x
area of square: As(x) = x2
length of the "square piece": 4x
length of "circle piece": 16 - 4x
We know that: C = 2 * pi * r => r = C/(2 * pi)
Area of cicle: Ac = pi * r2 = pi * [C/(2 * pi)]2 = pi * (C2/4 * pi2)
Ac = C2/4pi = (16 - 4x)2/4pi = 4(4 - x)2/4pi
Ac = (4 - x)2/pi
Ac(x) = (4 - x)2/pi
