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Answer:
The radius of the circle ,r= 1.43 m
The length of the side of square ,a= 2.77 m
Step-by-step explanation:
Given that
L= 20 m
Lets take radius of the circle =r m
The total parameter of the circle = 2π r
Area of circle ,A=π r²
The side of the square = a m
The total parameter of the square = 4 a
Area of square ,A'=a²
The total length ,L= 2π r+ 4 a
20 = 2π r+ 4 a
r=3.18 - 0.63 a
The total area = A+ A'
A" =π r² +a²
A"= 3.14(3.18 - 0.63 a)² + a²
For minimize the area
3.14 x 2(3.18 - 0.63 a) (-0.63) + 2 a = 0
3.14 x (3.18 - 0.63 a) (-0.63) + a = 0
-6.21 + 1.24 a + a=0
2.24 a = 6.21
a=2.77 m
r= 3.18 - 0.63 a
r= 3.18 - 0.63 x 2.77
r=1.43 m
Therefore the radius of the circle ,r= 1.43 m
The length of the side of square ,a= 2.77 m