Answer:
In explanation you see the answer but it I see it send it different so I just added a file so you can see clearly the way how this exercise works. Please, see the file attached
Explanation:
Let x = circumference of the circle
then
(53-x) = the perimeter of the square
and \frac{53-\times}{4} = the side of the square
and
\left(\frac{53-\times}{4}\right)^2 = the area of the square
:
Find the area of the circle using the circumference
find the radius (r)
2*pi*r = x
r = \frac{\times}{2*\mathbit{\pi}}
r = \frac{\times}{6.28}
Find the area of the circle
\mathbit{A}=\pi r^2
Replace r with \frac{\times}{6.28}
A = π * \left(\frac{\times}{6.28}\right)^2= * \left(\frac{\times^2}{39.48}\right)
cancel pi into 39.48
A = \left(\frac{\times^2}{12.566}\right)
Total area of circle and square
A = \left(\frac{\times^2}{12.566}\right)+\left(\frac{53-\times}{4}\right)^2 = \left(\frac{\times^2}{12.566}\right) + \left(\frac{{2809-106\times+\times}^2}{16}\right)
:
convert these fractions to decimal coefficients
A(x) = .0796x^2 + .0625x^2 - 6.625x + 175.5625
A(x) = .1421x^2 - 6.625x + 175.5625
:
Find the axis of symmetry of this quadratic equation (min area)
x = \frac{-\left(-6.625\right)}{2*.1421}
x = \frac{6.625}{.2842}
x = 23.31 cm is the circumference when they have min area
