Question 426053: Find the length and width of a rectangle that has the given perimeter and a maximum area.
Perimeter: 48 meters Answer by Gogonati(855) (Show Source):
You can put this solution on YOUR website! Solution:Denote the length of rectangle x m, since the perimeter is 48m then the width of rectangle is (24-x)m. We know that the area of rectangle is:
This function introduce a downward parabola.
We find the vertex of this parabola:
Since the length is 12m the width will be: 24-12=12m
We conclude that this rectangle has the maximum area when its shape is square of side 12m.
We find the value of area for x=12m : .
