Question

-Tracy has 36 feet of fencing to create a dog pen. Which dimensions should she use if she wants to have the most area?

Answer 1

The best area is a square. The perimeter of the square is 36 ft so the side is a quarter of this which is 9 ft. 9*9=81 sq ft. If we choose a rectangle with sides a and b, then a+b=18 ft. The area is ab. If we pick a=8 and b=10, the area would be 80 sq ft. If we pick 8.5 and 9.5 the area is 80.75 sq ft. Only when a=b=9 do we get the maximum area.