Question

For a rectangle with a perimeter 44 to have the largest area, what dimensions should it have?

Answer 1

let the length be l and breadth be b
perimeter=2(l+b)=44
so l+b=22
now Area A=l*b
in terms of l
b=22-l
so A=l*(22-l)
now differentiate A w.r.t l
dA/dl=22-2l
for finding the value of l for which area is max, equate dA/dl to 0
22-2l=0
l=11
this is the value of l for which area is max
b=22-l=22-11=11
so l =11 and b=11
area=121 unit^2