Math

posted by .

This is for grade 11 math, under quadratic extrema and roots.

Fred and Ginger have 24 m of fencing to enclose a garden at the back of their house. From the pictures you can see (shows a large rectangle for the house, with a smaller one attached on the bottom line, to the right) they want to fence only three sides of the garden. What are the dimensions of the garden having the biggest area they can enclose with their fence? What is the maximum area?
Hint: Define x to be the garden's width and get an equation for the part of the perimeter being fenced. Put this expression in an area formula and notice that your area formula becomes a quadratic function in x. (You know how to find the maximum of a quadratic function.)

Here's what I got so far.

Let x be the width.
Let L be the length.
Let A be the area.

2x + L = 24
L = 24 - 2x

A = Lx
A = (24 - 2x)X
= -2x(squared) + 24x

This is with my teacher's help. I just need to know how to get the answers, what my next steps should be, etc.

  • Math -

    well... break it down, first focus on 2x + L = 24
    L = 24 - 2x

    this should be your first step.

    What I did with this problem is that I rearanged the problem so it was easy.
    First ask youself what would be the max number that I could use to make x= a number times 2 = another number to = 24. I don't think this is the max you can go but so far i got L= 24- 2(2)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Vitaly and Jen have 24m of fencing to enclose a vegetable garden at the back of their house. What are the dimensions of the largest rectangular garden they could enclose with this length of fencing?
  2. Math

    P = 2l + 2w A = lw P = 4s A = s2 C = ðd A = ðr2 Use 3.14 for ð. Lawrence has planted a round flower garden in his back yard. The garden is 8 feet across. How many feet of fencing does Lawrence need to enclose the flower garden?
  3. Polynomials and quadratic application

    I want to make a rectangular garden by fencing in a area on the back of my house. Three sides of the rectangle will be fencing; the fourth side will be the side of the house. I have 60 feet of fence. What dimensions should I make the …
  4. MATH 11 help PLease!

    A rectangular garden is made at the side of the house. Part of the house forms one side of the fencing and divided into four equal plots. If 90m of fencing is available, determine the dimensions for the entire garden that will produce …
  5. 4th grade math

    Bryan is putting fencing around his new rectangular vegetable garden. He uses 140ft of fencing material. How wide is the garden?
  6. Math

    The Kulas have decided to enclose their rectangular garden. The length of the garden is 8 meters, and 30 meters of fencing is needed to enclose the garden. What is the width of the garden?
  7. Math help!

    Hilda has a rectangular garden by the river in front of her house. The area she uses for planting tomatoes is three times as large as that she uses for beets. If she has 270 yards of fencing material to enclose the garden to protect …
  8. math

    You have 540 feet of fencing to enclose a rectangular garden. You want the length of the garden to be 50 feet greater than the width. Find the length and width of the garden if you use all of the fencing.
  9. Algebra

    You are in the process of planning a garden in your back yard. The garden will be rectangular in shape. Determine the best length and width (in feet) for your garden and determine how many feet of fencing you will need to enclose the …
  10. Math

    Suppose that 32 feet of fencing is available to enclose a rectangular garden., one side of which will be against the side of a house. What dimensions of the garden will guarantee a maximum area?

More Similar Questions