Richard is building a rectangular backyard from 400 feet of fencing. The fencing must cover three sides of the backyard (the fourth side is bordered by Richard's house). What is the maximum area of this backyard?
The maximum will be a SQUARE (which is a rectangle ) of side length 400/3 ft
you should be able to calculate the area of the square now that you have the side length.....
Let two of the equal sides = x Let the other side = y
2x + y = 400 → y = 400 - 2x
Area = xy
A = x ( 400 - 2x)
A = 400x - 2x^2 take the derivative
A' = 400 - 4x
Set the derivative = 0
400 - 4x = 0
400 = 4x
x = 100
y = 400 -2x = 200
Max area = 100 * 200 = 20000 ft^2
See the graph of the Area function here.....https://www.desmos.com/calculator/pvjvhyciaz