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 side - length of square

The perimeter of a square $P = 4s$, where $s$ is the side - length. Given $P = 56$ cm, then $s=\frac{P}{4}=\frac{56}{4}=14$ cm.

Step2: Find diagonal length

For a square of side - length $s$, the length of the diagonal $d$ can be found using the Pythagorean theorem. In a square, if the side - length is $s$, and the diagonal is $d$, then $d^{2}=s^{2}+s^{2}=2s^{2}$. Substituting $s = 14$ cm, we get $d^{2}=2\times14^{2}=2\times196 = 392$. So, $d=\sqrt{392}\approx19.8$ cm.

Answer:

D. 19.8 cm