faye has 20 feet of fencing to make a rectangular pen for her dog.What is the largest area she can fence in?
20 feet
Let's see --
it could be 5 + 5 + 5 + 5
or 4 + 4 + 6 + 6
or 3 + 3 + 7 + 7
Find the areas of these pens.
A = length times width
So -- a 3 foot by 7 foot pen would be 21 square feet.
Find the areas of the other two pens. Which gives you the most square feet?
For a math question:
Make a table of width (W) and lengths (L) that add up to 20 for perimeter = 2(W+L).
Calculate the area for each line. Choose the biggest area.
Width Length Area
1 9 9
2 8 16
3 7 21
4 6 24
.....
8 2 16
9 1 9
For a calculus question:
Let W=width, then
(10-W)=length, and
Area=A(W)=W(10-W)=10W-W²
For maximum or minimum:
dA/dW=10-2W=0, or W=5
d²A/dW²=-2 <0 so maximum.
A(5)=5(10-5)=25 (maximum area)
hi im only in 4th grade so i really kind of need simple answers
Please see my answer. I'm sure you can figure out your answer using that information.
thanks ms.sue u rock
You're welcome, Alex. :-)
To find the largest possible area that Faye can fence in using the given 20 feet of fencing, she should create a rectangular pen where one side is twice the length of the other side. This is because the formula for the area of a rectangle is length multiplied by width, and to maximize the area while using a fixed perimeter, the rectangle should be as close to a square as possible.
Let's denote the length of the rectangular pen as L and the width as W. Since one side should be twice the length of the other side, we can set up the equation:
L = 2W
To find the maximum area, we need to express the perimeter in terms of a single variable. The perimeter of a rectangle is given by the formula:
Perimeter = 2L + 2W
Since Faye has 20 feet of fencing, we can write:
2L + 2W = 20
Substituting L = 2W into the equation, we can solve for W:
2(2W) + 2W = 20
4W + 2W = 20
6W = 20
W = 20/6
W = 3.33 (rounded to 2 decimal places)
Now that we have the value for W, we can find the length by substituting it back into L = 2W:
L = 2(3.33)
L = 6.66 (rounded to 2 decimal places)
The width is approximately 3.33 feet, and the length is approximately 6.66 feet, which adds up to a total of approximately 20 feet of fencing.
Finally, we can find the maximum area by multiplying the length and width:
Area = Length * Width
Area = 6.66 * 3.33
Area = 22.12 square feet (rounded to 2 decimal places)
Therefore, the largest area Faye can fence in with 20 feet of fencing is approximately 22.12 square feet.