Question

The perimeter of a square is 54cm. Find the length of a diagonal, rounding to the nearest tenth.
A.
182.3cm

B.
19.1cm

C.
13.5cm

D.
22.4cm

Answer 1

To find the length of the diagonal of a square when the perimeter is given, follow these steps:

1. **Calculate 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 of the square. Given that the perimeter is 54 cm, we can set up the equation:
\[
54 = 4s
\]
To find \( s \), divide by 4:
\[
s = \frac{54}{4} = 13.5 \text{ cm}
\]

2. **Calculate the length of the diagonal**:
The diagonal \( d \) of a square can be calculated using the formula:
\[
d = s\sqrt{2}
\]
Substituting \( s = 13.5 \) cm into the equation:
\[
d = 13.5\sqrt{2}
\]
Now, we need to calculate \( \sqrt{2} \):
\[
\sqrt{2} \approx 1.414
\]
Therefore:
\[
d \approx 13.5 \times 1.414 \approx 19.1 \text{ cm}
\]

3. **Round the result to the nearest tenth**:
The result is already at 19.1 cm.

The length of the diagonal of the square, rounded to the nearest tenth, is **19.1 cm**.

Thus, the answer is **B. 19.1cm**.