Question 559691
Karina has a piece of wire that is 16 inches long. Use this fact to answer the following questions. Round your answers to the nearest tenth. 
a. What will be the area inside a semicircle made from this wire?
Perimeter = (pi)d = 16 inches
d = 16/(pi)
radius = 8/(pi)
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Area = (pi)[8/(pi)]^2
Area = 64/(pi) sq. inches
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c. Suppose that Karina cuts the wire into 2 pieces to make 2 squares such that the area of 1 square is twice the area of the other. What is the side length of the larger square?
Let one piece be "x":
Other piece is "16-x"
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Areas:
1st square
side = x/4
Area = (x/4)^2
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2nd square:
side = (16-x)/4
Area = [(16-x)/4]^2
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Equation:
Area #1 = 2 Area #2
(x/4)^2 = 2[(16-x)/4]^2
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Multiply both sides by 16:
x^2 = 2(16-x)^2
x^2 = 2(256 - 32x + x^2)
x^2 = 512 - 64x + 2x^2
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x^2 - 64x +512 = 0
I graphed it to get x = 9.37 and x = 54.63
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Cheers,
Stan H.
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thanks!