To find the diagonal of a square frame with a perimeter of 48 inches, we first need to determine the length of one side of the square.
The formula for the perimeter \( P \) of a square is given by:
\[ P = 4s \]
where \( s \) is the length of one side. By rearranging the formula, we can find the side length:
\[ s = \frac{P}{4} = \frac{48}{4} = 12 \text{ inches} \]
Now, we can calculate the diagonal \( d \) of the square using the formula:
\[ d = s\sqrt{2} \]
Substituting the value of \( s \):
\[ d = 12\sqrt{2} \]
Calculating \( \sqrt{2} \) (approximately 1.414):
\[ d \approx 12 \times 1.414 \approx 16.97 \text{ inches} \]
Rounding this value gives approximately 17 inches.
Thus, the measurement of the diagonal of the frame is:
D. 17 inches.