What is the maximum area for a garden of 120 ft of fencing, when one side has a house on it that takes up 42 ft? What is the maximum area?

Answer 1

Assuming that the garden will be rectangular, the side opposite the house can be designated as H (which will also be 42 feet) and the other two sides as O. So, H+2O=120 -> 42+2O=120 -> 2O=78 -> O=39. Therefore, the garden area would be 42*39 or 1638 square feet

Answer 2

If one side must be 42 ft in length, and if the garden must be rectangular, then it will have two sides of 42 = 84

120 - 84 = 36 feet left for the two other sides.

36/2 = 18, so the other two sides are each 18 feet.