Problema Solution
a rectangular piece of land,bounded by one side by a river is to be fenced on the other three sides. What is the largest possible area that can be enclosed by 300 meters of fencing.. complete the square to find the maximum area
Answer provided by our tutors
Call the single side parallel to the river length x
Call the other two sides length y
x + 2y = 300
x = 300 - 2y
Area = xy
Combine equations:
Area = y(300 - 2y)
Area = -2y^2 + 300y
Area / -2 = y^2 - 150y
Area / -2 + 5625 = y^2 - 150y + 5625 (this step completes the square)
Area / -2 + 5625 = (y - 75)^2
Area / -2 = (y - 75)^2 - 5625
Area = 11250 - 2(y - 75)^2
In the above equation, it is clear that when y = 75, area is maximum, since any other value would reduce the maximum area, which is 11250.
So maximum area = 11250 square meters.