a rectangular yard is to be enclosed by a new fence on 3 sides and by an existing fence on the fourth side. the amount of new fencing to be used is 160 feet
To find the perimeter of the rectangular yard, we need to consider that the existing fence already covers one side. Let's assume the length of the rectangular yard is L and the width is W.
The perimeter formula for a rectangle is given by P = 2L + 2W. In this case, since the existing fence covers one side, we only need to add new fencing to the other three sides. Therefore, the new fencing required is 2L + 2W.
The problem states that the amount of new fencing to be used is 160 feet. So, we can set up the equation:
2L + 2W = 160
Divide both sides of the equation by 2 to simplify:
L + W = 80
This equation represents the relationship between the length and width of the rectangular yard. However, without any additional information or constraints, we can't determine the exact dimensions of the yard.
To solve for specific values of L and W, we would need more information such as the relationship between the length and width (e.g., if they are equal, or if one is double the other) or the total area of the yard.
Thus, the information provided allows us to set up the equation but does not provide enough details to solve for the specific dimensions of the rectangular yard.