a rectangular garden has an area of 250 square meters is to be located next to a building and fenced on three sides, with the building acting as a fence on a fourth side

Question

Find the dimensions of the garden that will minimize the amount of required

Answer 1

Area = A = LW = 250

L= 250/W

L+2W = length of the fence = F = 250/W + 2W

F'= -250/W^2 + 2 = 0

2W^2 = 250

W^2 = 125

W = sqr125 = 5sqr5 = about 5(2.2) = 11 feet

L = 250/5sqr5 = 50/sqr5 = 50(sqr5)/5 = 10sqr5 = about 22 feet

22x11 = 242.

sides that minimize fence length are a little over 11 x 22 feet

or exactly 5sqr5 by 10sqr5. The length is twice the width