To find the width \( w \) in terms of the perimeter \( P \), let's start with the given formula for the perimeter of the rectangle:
\[ P = 8w + 10 \]
We want to solve this equation for \( w \). First, we can isolate \( 8w \) by subtracting 10 from both sides:
\[ P - 10 = 8w \]
Next, we divide both sides by 8 to solve for \( w \):
\[ w = \frac{P - 10}{8} \]
Now, we can rearrange it further to get \( w \) in a more standard form. If we want to bring \( P \) to the other side:
\[ w = \frac{1}{8}P - \frac{10}{8} \] \[ w = \frac{1}{8}P - \frac{5}{4} \]
However, looking at the provided options, none directly match this expression.
Now, let's rearrange the equation \( P = 8w + 10 \) to directly isolate \( w \) in terms of \( P \):
Starting from: \[ P = 8w + 10 \] Subtract 10: \[ P - 10 = 8w \] Divide by 8: \[ w = \frac{P - 10}{8} \] Since none of the options directly match, let’s explore them with the perimeter:
- \( A) w = P - 54 \) => Incorrect since it doesn't align with our derived formula.
- \( B) w = P - 108 \) => Incorrect.
- \( C) w = -P + 108 \) => Incorrect.
- \( D) w = 18P−10 \) => Incorrect.
It seems we are looking at incorrect formulations in the options. However, with the derived relationship \( w = \frac{P - 10}{8} \), if we multiply the equation by 8,
this becomes \( 8w = P - 10 \).
None of the options appear to correctly derive from this while conforming to standard forms.
If you want precise clarity regarding the question, please double-check or specify, but according to the calculation: \[ \text{The calculation leads to } w = \frac{1}{8}(P - 10). \]
Thus the correct relationship for \( w \) is most accurately derived from our manipulation of the perimeter. This indicates none of the listed choices provides an accurate formula based on the given perimeter formula. Proceeding with \( w \) to confirm understanding can also direct attention if misinterpretation has occurred.