+208 Richard is building a rectangular backyard from 360 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?
+128407 Let two of the sides = x and the remaining side = y
Perimeter = 2x + y
360 = 2x + y
y = 360 -2x
Area = xy
Area = x ( 360 -2x)
Area = -2x^2 + 360x
The area will be maximized when x = -360 / (2 * -2) = 90
And the max area =
xy =
90 ( 360 - 2 *90) =
90 ( 180) =
16200 ft^2
