You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. how much should each side be to maximize your total area? what will the total area be for the garden? find the length, width, and area of your garden that will maximize its total area.

length:
width:
area:

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

we have

so

simplify

------> equation A

Remember that the area of rectangle is equal to

----> equation B

substitute equation A in equation B

----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point

see the attached figure

so

Find the value of y

The garden is a square

the area is equal to

----> is equal to the y-coordinate of the vertex is correct

I graphed the given points and used Pythagorean theorem to get the value of each side of the rhombus.

Each side of the rhombus served as the hypotenuse of the imaginary right triangle formed in the graph. The diagonals formed are mutually bisecting and have cut each diagonal in equal parts.

Pls. see attached graph.