Choose some other possibilities for the dimensions of the pen using all 20
feet of the fencing for the 3 sides that are needed. Make a table that uses
the distance d, away from the house (in the diagram it’s 5 feet or the
width) as input and the area as output.
d A
5 ?
To find the other possibilities for the dimensions of the pen using all 20 feet of fencing, we know that the perimeter of the pen should add up to 20 feet. Additionally, we are given that one of the sides of the pen is 5 feet, which is the width (d) away from the house.
Let's denote the length of the pen as L and the remaining side as W.
Since we have 3 sides that add up to 20 feet, we can write the equation:
L + W + 5 = 20
Simplifying the equation, we get:
L + W = 15
Now, we need to express the area (A) of the pen as a function of the distance (d) away from the house. The area of a rectangle is given by the formula:
A = L * W
Substituting the equation for L from above, we get:
A = (15 - W) * W
Now, we can create a table using different values for W and calculating the corresponding area. We'll substitute each value of W into the equation for A to find the area.
Using different values for W, we can calculate the area (A) as follows:
W | A
----------
1 | (15 - 1) * 1
2 | (15 - 2) * 2
3 | (15 - 3) * 3
4 | (15 - 4) * 4
5 | (15 - 5) * 5
6 | (15 - 6) * 6
7 | (15 - 7) * 7
8 | (15 - 8) * 8
9 | (15 - 9) * 9
10 | (15 - 10) * 10
11 | (15 - 11) * 11
12 | (15 - 12) * 12
13 | (15 - 13) * 13
14 | (15 - 14) * 14
15 | (15 - 15) * 15
Now, you can fill in the respective values of W and calculate the corresponding areas (A) using the formula we derived.
Let me know if there is anything else I can assist you with!