To determine the length of a rectangle when the perimeter and the width are known, we can use the formula for the perimeter of a rectangle, which is given by:
- Perimeter (P) = 2 * (Length (l) + Width (w))
In this case, we already know the perimeter and the width:
- Perimeter (P) = 34 units
- Width (w) = 65 units
Now, we can plug these values into the perimeter formula:
- 34 = 2 * (l + 65)
Next, we will simplify the equation:
- First, divide both sides by 2 to isolate the expression in parentheses:
- 17 = l + 65
- Now, subtract 65 from both sides to solve for the length (l):
- 17 – 65 = l
- l = -48
However, this result indicates that there was likely an error in the provided values, as a rectangle cannot have a negative length. Usually, in a real-world scenario, dimensions such as width should be less than the total perimeter to maintain a valid rectangle. Please double-check the dimensions and the perimeter provided to ensure they make sense.
In summary, the standard relationship for a rectangle’s perimeter does not yield a sensible value in this case, and thus we need to reevaluate the inputs.