Answer:
The dimensions of the rectangular corral producing the greatest enclosed area is a square of 80 ft x 80 ft
Step-by-step explanation:
Let
x -----> the length of the rectangular corral in feet
y -----> the width of the rectangular corral in feet
we know that
The area of the rectangular corral is equal to
-----> equation A
The perimeter of the rectangular corral is equal to
so
Simplify
-----> equation B
substitute equation B in equation A
This is a vertical parabola open downward
The vertex is a maximum
The x-coordinate of the vertex represent the length for the maximum area
The y-coordinate of the vertex represent the maximum area
Convert the quadratic equation in vertex form
Factor -1
Complete the square
Rewrite as perfect squares
The vertex is the point (80,6,400)
so
The maximum area is 6,400 ft^2
<em>Find the value of y</em>
---->
therefore
The dimensions of the rectangular corral producing the greatest enclosed area is a square of 80 ft x 80 ft