SOLUTION: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 48 meters

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 :
.

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