Answer to Question #18718 in Calculus for hsd

Question

Find the dimensions of a rectangle with area 2500 m^2 whose perimeter is as small as possible. List the dimensions in non-decreasing order.

........................m

........................m

Answer 1

the area of rectangle with sides a and b is equal to S=ab
then b=S/a.

perimeter is
p = 2(a+b) = 2 (a+S/a) = 2(a+2500/a)
this function is has minimum at a=50.

hence, a=b=50 to be perimeter as small as possible.