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.

Guest Feb 25, 2015

#1**+5 **

length of rope: 16 ft

length of one side of the square: x

area of square: A_{s}(x) = x^{2}

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 * r^{2} = pi * [C/(2 * pi)]^{2} = pi * (C^{2}/4 * pi^{2})

Ac = C^{2}/4pi = (16 - 4x)^{2}/4pi = 4(4 - x)^{2}/4pi

Ac = (4 - x)^{2}/pi

Ac(x) = (4 - x)^{2}/pi

Tetration
Feb 25, 2015

#1**+5 **

Best Answer

length of rope: 16 ft

length of one side of the square: x

area of square: A_{s}(x) = x^{2}

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 * r^{2} = pi * [C/(2 * pi)]^{2} = pi * (C^{2}/4 * pi^{2})

Ac = C^{2}/4pi = (16 - 4x)^{2}/4pi = 4(4 - x)^{2}/4pi

Ac = (4 - x)^{2}/pi

Ac(x) = (4 - x)^{2}/pi

Tetration
Feb 25, 2015