Question

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.

Answer 1

1st piece: x feet
2nd piece: 8-x feet
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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
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Use the 10-x piece to form square:
side = (1/4pi)(10-x)
Area = side^2 = (1/16)(10-x)^2

Hope this helps! :)