Question

Hello I need help with this, Don Manuel has 600m of fence to build a rectangular-shaped corral. You will take advantage of a very long wall as one of the sides of the pen, that is, on the side of the wall you will not use fence. What should be the dimensions of the pen with maximum area among all those that use 600m of fence?​

Answer 1

Answer: If the wall is 300 meters long, the dimensions of the fence with the maximum area will be 300 × 150 = 45000 m²

Explanation:

try combinations in a chart

190 × (600-190)/2 = 38950 = 190 × 205 increasing area

200 × (600-200)/2 = 40000 = 200 × 200

220 × (600-220)/2 = 41800 == 220 × 190

240 × (600-240)/2 = 43200 == 240 × 180

260 × (600-260)/2 = 44200 == 260 × 170

280 × (600-280)/2 = 44800 . == 280 × 160

300 × (600-300)/2 = 45000 == 300 × 150 Maximum Area

310 × (600-310)/2 = 44950 . == 310 × 145 decreasing area

320 × (600-320)/2 = 44800 . == 320 × 140