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

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!