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 formula of a square is \(P = 4s\) (where \(P\) is perimeter and \(s\) is side - length). Given \(P=56\) cm, then \(s=\frac{P}{4}\).
\(s=\frac{56}{4}=14\) cm.

Step2: Use the Pythagorean theorem to find the diagonal length

In a square, if the side - length is \(s\) and the diagonal length is \(d\), by the Pythagorean theorem \(d^{2}=s^{2}+s^{2}\) (since the two sides of the right - triangle formed by the diagonal are equal in a square). So \(d^{2}=2s^{2}\).
Substitute \(s = 14\) into the formula: \(d=\sqrt{2s^{2}}=s\sqrt{2}\).
\(d = 14\sqrt{2}\approx14\times1.414 = 19.796\approx19.8\) cm.

Answer:

19.8 cm