Tyler has 120 linear feet of fencing to put around his garden. if he uses the fence to border a rectangular garden, what is the maximum area his garden can be? answer should have units written out such as yards, square centimeters or cubic inches.

The maximum area is

Step-by-step explanation:

Let

x----> the length of rectangle

y---> the width of rectangle

we know that

The perimeter of rectangle is equal to

we have

so

------> 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 of the graph is the maximum area of the garden and the x-coordinate is the length for the maximum area

using a graphing tool

The vertex is the point

see the attached figure

Find the value of y

----->  

The dimensions of the rectangular garden is by

For a maximum area the garden is a square

The maximum area is

-1/2 +2

step-by-step explanation: