Question

The perimeter of a rectangle is 4040 yards. what are the dimensions of the rectangle with maximum area?

Answer 1

Let x be the length and y be the width2x + 2y = 40x + y = 20change that into y = mx + b formy= 20 – x
Area =xy = x (20-x) = 20x - x^2Area=-x^2+20xcomplete the square:Area=-(x^2 – 20x + 100) +100=-(x - 10)^2 + 100This is an calculation of a parabola that opens downward with vertex at (10,100), which means maximum area of 100 happens when x, the length=10)Dimensions of the rectangle with maximum area? 10 yds. by 10 yds., a square.