SOLUTION: 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

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Question 764190: 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 by stanbon(75887) About Me  (Show Source):
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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.
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1st piece: x feet
2nd piece: 10-x feet
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Use the "x" piece to form a circle:
Circumference = "x".
2(pi)*radius = x
radius = x/(2pi)
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So, Area = pi[x/(2pi)]^2 = x^2/(4pi) = (1/4pi)x^2
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Use the 10-x piece to form square:
side = (1/4)(10-x)
Area = side^2 = (1/16)(10-x)^2
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Cheers,
Stan H.