Optimization math problem

Question

Frank needs to make a rectangular garden with an area of 625 feet and he wants to figure out what is the least amount of fencing he needs to do this. Find the dimensions of the smallest amount of fencing needed to produce this garden.

Answer 1

Lw = 625

P = 2L + 2w

= 2L + 2(625/L)

= (2L^2 + 1250)/L

0 = dP/dL = {L(4L) - (2L^2 + 1250) }/ L^2

0= 4L^2 - 2L^2 - 1250

0 = 2L^2 - 1250

L^2 = 625

L=25 <--- throws negative away

w=25

square with side 25, so 100 feet

Answer 2

25*4=100 feet......................