Question

the perimeter of a square is 56 cm. what is the approximate length of its diagonal?
○ 10.6 cm
○ 14.0 cm
○ 15.0 cm
○ 19.8 cm

Explanation:

Step1: Find the side length of the square.

The perimeter of a square is given by \( P = 4s \), where \( s \) is the side length. We know \( P = 56 \) cm, so we solve for \( s \):
\( 4s = 56 \)
\( s=\frac{56}{4}=14 \) cm.

Step2: Use the Pythagorean theorem to find the diagonal.

In a square, the diagonal \( d \) forms a right triangle with two sides, so by the Pythagorean theorem \( d^{2}=s^{2}+s^{2}=2s^{2} \).
Substituting \( s = 14 \) cm:
\( d^{2}=2\times(14)^{2}=2\times196 = 392 \)
Then \( d=\sqrt{392}\approx19.8 \) cm.

Answer:

19.8 cm (corresponding to the option with 19.8 cm)