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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

Best Answer 

 #1
avatar+808 
+5

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

Tetration  Feb 25, 2015
 #1
avatar+808 
+5
Best Answer

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

Tetration  Feb 25, 2015

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