Mathematics
Mathematics
Problem
A rectangular field will be enclosed on three sides with 100 meters of fencing; the fourth side borders a straight river and requires no fence. Which of the following is the maximum area, in square meters, that can be enclosed? a) b) c) d)Intuitive explanation
This is an optimization problem where you're balancing two competing constraints: you have a fixed amount of fencing (100 m) to distribute among three sides, and you want to maximize the resulting area. The key insight is to express area as a function of one variable using your constraint, then find where that function peaks. Since the river forms one side, you're essentially choosing how to split your 100 m between the two perpendicular sides and one parallel side—and the proportions matter for the maximum.
Intuitive explanation
This is an optimization problem where you're balancing two competing constraints: you have a fixed amount of fencing (100 m) to distribute among three sides, and you want to maximize the resulting area. The key insight is to express area as a function of one variable using your constraint, then find where that function peaks. Since the river forms one side, you're essentially choosing how to split your 100 m between the two perpendicular sides and one parallel side—and the proportions matter for the maximum.