the perimeter of a square is 56 cm. what is the approximate length of its diagonal?\n10.6 cm\n14.0 cm\n15.0…

Answer:

D. 19.8 cm

Explanation:

Step1: Find side - length of square

Let side - length be $s$. Perimeter $P = 4s$. Given $P = 56$ cm, then $4s=56$, so $s=\frac{56}{4}=14$ cm.

Step2: Use Pythagorean theorem for diagonal

In a square, if side - length is $s$ and diagonal is $d$, by Pythagorean theorem $d^{2}=s^{2}+s^{2}$. Substitute $s = 14$ cm, we get $d^{2}=14^{2}+14^{2}=196 + 196=392$. Then $d=\sqrt{392}\approx19.8$ cm.