3)for maximum area(constant perimeter)
put x=0 or y=0
hence maximum area will be p^2/(4pi)
though not asked but minimum area will be
[p^2/4(pi)^2][pi/2+1][this can be obtained using calculus]
a. Find a formula for the area
b. find a formula for the perimeter
c. find the dimensions x and y that maximize the area given that the perimeter is 100 .
* See attachment for details!!!
I know that this figure is composed of 4 semicircles and one rectangle ; the area of the rectangle is xy , and the area of the semicircle is 1/2pir^2. The perimeter of the rectangle is 2x + 2y , but I'm not sure how to apply the perimeter of the semicircles to this problem. On the other hand , the constraint I should use is in part c ; however , I need to find out a and b before that. I really would appreciate help for this application .Thanks for your time !!!
The perimeter, however, has nothing to do with the perimeter of the rectangle. It is, instead, the total perimeter of the two circles, .
You are then given that so . Replace y by that in the formula for the area, . Minimize that.