the perimeter of a square frame is 48 inches.

What is the approximate measurement of the diagonal of the frame
A. 12 inches
B. 13 inches
C. 15 inches
D. 17 inches

1 answer

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.