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

For a square with side - length \(s\), if the diagonal length is \(d\), by the Pythagorean theorem \(d^{2}=s^{2}+s^{2}\) (since in a square, the two sides and the diagonal form a right - triangle with legs of length \(s\)). So \(d^{2}=2s^{2}\). Substitute \(s = 14\) into the formula:

$$d=\sqrt{2s^{2}}=s\sqrt{2}$$

$$d = 14\times\sqrt{2}\approx14\times1.414 = 19.796\approx19.8$$

cm.

Answer:

19.8 cm