To find out how many feet of fencing George will need for the dog run, we first need to find the width, which is expressed as \( (30 - x) \) feet.
The area of the dog run is given as 240 square feet, and we know that the area is calculated using the formula:
\[ A = l \times w \]
Substituting the given length and width:
\[ 240 = 30 \times (30 - x) \]
To solve for \( (30 - x) \):
\[ 240 = 30(30 - x) \] \[ 240 = 900 - 30x \] \[ 30x = 900 - 240 \] \[ 30x = 660 \] \[ x = \frac{660}{30} \] \[ x = 22 \]
Now we can find the width \( w \):
\[ w = 30 - x = 30 - 22 = 8 \text{ feet} \]
Next, we can calculate the perimeter \( P \) of the dog run that needs the fencing. Since George is using his house as one side, the perimeter is given by the other three sides:
\[ P = 2l + w \]
Substituting the values of length and width:
\[ P = 2(30) + 8 \] \[ P = 60 + 8 \] \[ P = 68 \text{ feet} \]
Therefore, George will need 68 feet of fencing for the dog run. The correct answer is:
68 feet.