Answer:
23.62 cm
Step-by-step explanation:
The question asking for a condition when the total area of the square and the circle(A) is minimum/lowest. To find the lowest area you can get, you have to differentiate the formula for the total area(A).
The wire is 77cm long, let's say x is the square side and r is the circle radius. Then it will be
77cm= 4x + 2 * π * r
4x= 77cm - 2 * π * r
x= (77cm - (π * r ))/4
Square area is x^2 while circle area is π *r^2. Total area will be:
A= square area + circle area
A== x^2 + π *r^2
A= ( (77 - (π r ))/4 ) ^2 + π *r^2
A=(5929- (144 * π r ) + π^2 r^2)/ 16 + π *r^2
A= 370.56 - 9 π r + π^2 r^2/16 + π *r^2
A= 370.56 - 28.26 r + 0.616r^2 + 3.14*r^2 =
A= 370.56 - 28.26 r + 3.756 r^2
Differentiate the equation to find the lowest point
370.56 - 28.26 r + 3.756 r^2
- 28.26 + 7.512 r = 0
r= 28.26 / 7.512
r = 3.76 cm
Radius of circle when A minimum is 3.76cm, then the perimeter will be: 2 * π *3.76= 23.62 cm
