Answer:
Step-by-step explanation:
The area of a triangle is given by the product between length and width:
(1)
where
L is the length
w is the width
The perimeter of the rectangle is given by
In this problem, we know that the perimeter of the rectangle is fixed, and it is
So we have:
Which can be rewritten as
If we substitute this into the formula of the area, (1), we get:
To maximize the area, we have to calculate its derivative and require it to be equal to zero:
Calculating the derivative,
And requiring it to be zero, we find:
Which means also
So,
L = 18 feet
w = 18 feet
So the maximum area is achieved when the rectangle has actually the shape of a square.
In such case, the area is:
So, this is the maximum area.