Can you please help me figure out what to do? ... here is the question ... I have 20 ft of fencing to make a rectangular pen for my dog. What is the largest area that I can fence in? ... Not sure what to do ... thank you!
The dimensions of your pen could be
2 feet by 8 feet
or
3 feet by 7 feet
or
4 feet by 6 feet
or
5 feet by 5 feet
To find the area, multiply the length times the width. Which set of dimensions gives you the largest area?
If you post your answer, we'll be glad to check it.
Thank you very much! I got it, 25 square feet Is that right?
right.
The exact question is Faye has 20 feet of fencing to make a rectngular pen for her dog.What is the largest area she can fence in?
Answer:__ square feet
Yea you guys are right! --25
Mrs. Griffen g.e teacher at jle
In n.c
rectangular**
Of course, I would be happy to help you solve this problem! To find the largest area that you can fence in with 20 ft of fencing, we need to determine the dimensions of the rectangular pen that will maximize the area.
Let's assume the length of the rectangular pen is "L" and the width is "W". To maximize the area, we should choose the length and width that will use up the entire 20 ft of fencing while maintaining the rectangular shape.
We know that for a rectangle, the perimeter is given by the equation: P = 2L + 2W, where P represents the perimeter. In this case, the perimeter is equal to 20 ft.
Using this information, we can set up an equation: 2L + 2W = 20. This equation represents the constraint that the perimeter of the pen is equal to 20 ft.
To find the largest area, we need to express the area of the pen in terms of a single variable. The area of a rectangle is given by the equation: A = L * W, where A represents the area.
Using the equation we derived for the perimeter, we can express the width in terms of the length: W = (20 - 2L) / 2.
Now we can substitute this expression for W into the equation for the area: A = L * ((20 - 2L) / 2).
Next, simplify the equation for the area: A = 10L - L^2.
To find the maximum area, we need to find the value of L that maximizes the equation. One way to do this is by finding the vertex of the quadratic equation.
To find the vertex, we can use the formula: L = -b / (2a), where the equation is in the form of ax^2 + bx + c = 0. In our case, a = -1, b = 10, and c = 0.
Substituting the values into the formula, we have: L = -10 / (2*(-1)) = -10 / -2 = 5.
So, the length that maximizes the area is 5 ft. Now, we can substitute this value back into the equation for the width: W = (20 - 2(5)) / 2 = 5 ft.
Therefore, the largest area that you can fence in with 20 ft of fencing is 5 ft by 5 ft, which gives an area of 25 square feet.