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 the perimeter and \(s\) is the 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 in a right - triangle formed by two adjacent sides and the diagonal of the square, \(a = s\), \(b = s\) and \(c = d\)).
Substitute \(s = 14\) into the formula: \(d^{2}=14^{2}+14^{2}=196 + 196=392\).
Then \(d=\sqrt{392}\). We can rewrite \(392\) as \(392=49\times8\), so \(d=\sqrt{49\times8}=\sqrt{49}\times\sqrt{8}=7\times2\sqrt{2}\approx7\times2\times1.414 = 19.796\approx19.8\) cm.

Answer:

19.8 cm