Question

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

Answer 1

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**.