Question
The perimeter of a square is 54 cm. Find the length of a diagonal, rounding to the nearest tenth.
22.4 cm
13.5 cm
19.1 cm
182.3 cm
22.4 cm
13.5 cm
19.1 cm
182.3 cm
Answers
GPT-4o mini
To find the length of the diagonal of a square, we first need to determine the length of one side of the square using the perimeter.
The formula for the perimeter \( P \) of a square is given by:
\[
P = 4s
\]
where \( s \) is the length of one side of the square.
Given that the perimeter is 54 cm, we can solve for \( s \):
\[
54 = 4s
\]
Dividing both sides by 4, we get:
\[
s = \frac{54}{4} = 13.5 \text{ cm}
\]
Next, we can find the diagonal \( d \) of the square using the formula:
\[
d = s\sqrt{2}
\]
Substituting \( s = 13.5 \text{ cm} \):
\[
d = 13.5\sqrt{2}
\]
Now, we can calculate \( \sqrt{2} \) (approximately 1.414):
\[
d \approx 13.5 \times 1.414 \approx 19.1 \text{ cm}
\]
Rounding to the nearest tenth, the length of the diagonal is approximately \( 19.1 \text{ cm} \).
Thus, the answer is:
\[
\boxed{19.1 \text{ cm}}
\]
The formula for the perimeter \( P \) of a square is given by:
\[
P = 4s
\]
where \( s \) is the length of one side of the square.
Given that the perimeter is 54 cm, we can solve for \( s \):
\[
54 = 4s
\]
Dividing both sides by 4, we get:
\[
s = \frac{54}{4} = 13.5 \text{ cm}
\]
Next, we can find the diagonal \( d \) of the square using the formula:
\[
d = s\sqrt{2}
\]
Substituting \( s = 13.5 \text{ cm} \):
\[
d = 13.5\sqrt{2}
\]
Now, we can calculate \( \sqrt{2} \) (approximately 1.414):
\[
d \approx 13.5 \times 1.414 \approx 19.1 \text{ cm}
\]
Rounding to the nearest tenth, the length of the diagonal is approximately \( 19.1 \text{ cm} \).
Thus, the answer is:
\[
\boxed{19.1 \text{ cm}}
\]