Respuesta :
The wire should cut at a distance of 33.6
For given question,
Let x be the length of one side of the square.
so, the Perimeter of a square = 4x
For the remaining length of (60 - x) we make a circle.
We know that the Circumference of a circle = 2πr
So, 4x + 2πr = 60
⇒ 2πr = 60 - 4x
⇒ r = (60 - 4x)/2π
⇒ r = (30 - 2x)/π
The area of the square would be,
[tex]A_s=x^{2}[/tex]
And the area of the circle would be,
[tex]\Rightarrow A_c=\pi (\frac{30-2x}{\pi} )^2\\\\\Rightarrow A_c=\frac{(30-2x)^2}{\pi}[/tex]
Thus summing the areas we get,
[tex]\Rightarrow A=A_s+A_c\\\\\Rightarrow A=x^{2} +\frac{(30-2x)^2}{\pi}[/tex]
To find the critical points we differentiate the given area with respect to 'x'
Thus we have,
[tex]\Rightarrow \frac{dA}{dx}=\frac{d[x^{2} +\frac{(30-2x)^2}{\pi}]}{dx}\\\\\Rightarrow 0=2x - \frac{4 (30-2x)}{\pi} \\\\\Rightarrow 2x = \frac{4 (30-2x)}{\pi}\\\\\Rightarrow x = \frac{60}{\pi}-\frac{4x}{\pi} \\\\\Rightarrow x (1+ \frac{4}{\pi})=\frac{60}{\pi} \\\\\Rightarrow x=8.4[/tex]
Thus the perimeter of square would be, 33.6
And the circumference of circle would be,
60 - 33.6 = 26.4
Thus, cut the wire at a distance of 33.6 and draw this length into a square and the remaining 26.4 into a circle.
Therefore, the wire should cut at a distance of 33.6
Learn more about the area of the circle and the area of the square here:
https://brainly.com/question/22964077
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