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March 4, 2015

March 4, 2015

Posted by **Dan** on Monday, November 19, 2012 at 12:28pm.

- calculus -
**Reiny**, Monday, November 19, 2012 at 2:24pmlet each side of the triangle be 4x (you will see why ...)

then each side of the square is 3x (ahh, how clever)

height of the triangle is 2√3x , by Pythagorus

let the radius of the circle be r

2πr + 24x = 100

πr = 50 - 12x

r = (50-12x)/π

total area (T) = πr^2 + 9x^2 + (1/2)(4x)(2√3x)

= π(50-12x)^2/π^2 + 4√3x^2

= (2500 - 1200x + 144x^2)/π + 9x^2 + 4√3x^2

d(T)/dx = -1200/π + 288x/π + 18x + 8√3x

= 0 for a min of T

timex π

-1200 + 288x + 18πx + 8√3π x=0

x(288 + 18π + 8√3π) = 1200

x = 3.092

r = 4.104

so diameter of circle is 8.21

perimeter of rectangle is 12x = 37.106

perimeter of square is 37.106

check:

2πr + 12x + 12x = 100

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